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Papers & Technical Reports

(Papers by Topics)

| 2024+ | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010- |
  Tony Cai

       Technical Reports

  1. Cai, T. T. & Kim, D. (2024).
    Transfer learning for covariance matrix estimation: Optimality and adaptivity.
    Technical report.
  2. Cai, T. T., Chakraborty, A., & Vuursteen, L. (2024).
    Federated nonparametric hypothesis testing with differential privacy constraints: Optimal rates and adaptive tests.
    Technical report.
  3. Auddy, A., Cai, T. T., & Chakraborty, A. (2024).
    Minimax and adaptive transfer learning for nonparametric classification under distributed differential privacy constraints.
    Technical report.
  4. Cai, T. T., Xia, D., & Zha, M. (2024).
    Optimal differentially private PCA and estimation for spiked covariance matrices.
    Technical report.
  5. Auddy, A., Cai, T. T., & Li, H. (2024).
    Regressing multivariate Gaussian distribution on vector covariates for co-expression network analysis.
    Technical report.
  6. Zhang, L., Ma, R., Cai, T. T., & Li, H. (2024).
    Estimation, confidence intervals, and large-scale multiple testing for high-dimensional mixed linear regression.
    Technical report.
  7. Cai, T. T., Chakraborty, A., & Vuursteen, L. (2023).
    Optimal federated learning for nonparametric regression with heterogenous distributed differential privacy constraints.
    Technical report.
  8. Wu, R., Zhang, L., & Cai, T. T. (2023).
    Supervised topic modeling: Optimal estimation and statistical inference.
    Technical report.
  9. Cai, T. T., Wang, Y., & Zhang, L. (2023).
    Score attack: A lower bound technique for optimal differentially private learning.
    Technical report.
  10. Cai, T.T. & Pu, H. (2022).
    Transfer learning for nonparametric regression: Non-asymptotic minimax analysis and adaptive procedure.
    Technical report.
  11. Chakrabortty, A., Lu, J., Cai, T. T., & Li, H. (2019).
    High dimensional M-estimation with missing outcomes: A semi-parametric framework.
    Technical report.
  12. Cai, T. T. & Yuan, M. (2014).
    Rate-optimal detection of very short signal segments.
    Technical report.
  13. Cai, T. T. & Yuan, M. (2010).
    Nonparametric covariance function estimation for functional and longitudinal data.
    Technical Report.

     

    2024+

  14. Liang, Z., Cai, T.T., Sun, W., & Xia, Y. (2024+).
    A locally adaptive algorithm for multiple testing with network structure.
    Statistica Sinica, to appear.
  15. Li, S., Cai, T.T., & Li, H. (2024+).
    Statistical inference for high dimensional regression with proxy data.
    Statistica Sinica, to appear.
  16. Rakshit, R., Wang, Z., Cai, T. T., & Guo, Z.(2024+).
    SIHR: Statistical inference in high-dimensional linear and logistic regression models.
    The R Journal, to appear.
  17. Wang, S., Yuan, B., Cai, T. T., & Li, H. (2024).
    Phylogenetic association analysis with conditional rank correlation.
    Biometrika 111, 881-902.
  18. Cai, T. T., Ke, Z. T., & Turner, P. (2024).
    Testing high-dimensional multinomials with applications to text analysis.
    Journal of the Royal Statistical Society, Series B 86, 922-942.
  19. Li, S., Zhang, L., Cai, T.T., & Li, H. (2024).
    Estimation and inference for high-dimensional generalized linear models with knowledge transfer.
    Journal of the American Statistical Association 119, 1274-1285.
  20. Cai, T. T. & Wei, H. (2024).
    Distributed Gaussian mean estimation under communication constraints: Optimal rates and communication-efficient algorithms.
    Journal of Machine Learning Research 25, 1-63.
  21. Cai, T.T., Kim, D., & Pu, H. (2024).
    Transfer learning for functional mean estimation: Phase transition and adaptive algorithms.
    The Annals of Statistics 52, 654-678.
  22. Ma, R., Guo, Z., Cai, T. T., & Li, H. (2024).
    Statistical inference for genetic relatedness based on high-dimensional logistic regression.
    Statistica Sinica 34, 1023-1043.
  23. Cai, T.T., Chen, R., & Zhu, Y. (2024).
    Estimation and inference for minimizer and minimum of convex functions: Optimality, adaptivity, and uncertainty principles.
    The Annals of Statistics 52, 392-411.
  24. Cai, C., Cai, T.T., & Li, H. (2024).
    Transfer learning for contextual multi-armed bandits.
    The Annals of Statistics 52, 207-232.
  25. Cai, T.T. & Ma, R. (2024).
    Matrix reordering for noisy disordered matrices: Optimality and computationally-efficient algorithms.
    IEEE Transactions on Information Theory 70, 509-531.

     

    2023

  26. Cai, T. T., Guo, Z., & Xia, Y. (2023).
    Statistical inference and large-scale multiple testing for high-dimensional regression models (with discussion).
    Test 32, 1135-1171.
  27. Li, S., Cai, T. T., & Li, H. (2023).
    Transfer learning in large-scale Gaussian graphical models with false discovery rate control.
    Journal of the American Statistical Association 118, 2171-2183.
  28. Wu, R., Zhang, L., & Cai, T. T. (2023).
    Sparse topic modeling: Computational efficiency, near-optimal algorithms, and statistical inference.
    Journal of the American Statistical Association 118, 1849-1861.
  29. Xia, Y. & Cai, T. T. (2023).
    Discussion of "A Scale-Free Approach for False Discovery Rate Control in Generalized Linear Models" by Dai, Lin, Xing, and Liu
    Journal of the American Statistical Association 118, 1569-1572.
  30. Cai, T. T., Guo, Z., & Ma, R. (2023).
    Statistical inference for high-dimensional generalized linear models with binary outcomes.
    Journal of the American Statistical Association 118, 1319-1332.

     

    2022

  31. Li, S., Cai, T. T., & Li, H. (2022).
    Inference for high-dimensional linear mixed-effects models: A quasi-likelihood approach.
    Journal of the American Statistical Association 117, 1835-1846.
  32. Cai, T.T. & Ma, R. (2022).
    Theoretical foundations of t-SNE for visualizing high-dimensional clustered data.
    Journal of Machine Learning Research 23, 1-54.
  33. Cai, T. T., Zhang, A., & Zhou, Y. (2022).
    Sparse group Lasso: Sample complexity, optimal rate, and statistical inference.
    IEEE Transactions on Information Theory 68, 5975-6002.
  34. Cai, T. T., Sun, W., & Xia, Y. (2022).
    LAWS: A locally adaptive weighting and screening approach to spatial multiple testing.
    Journal of the American Statistical Association 117, 1370-1383.
  35. Cai, T.T. & Pu, H. (2022).
    Stochastic continuum-armed bandits with additive models: Minimax regrets and adaptive algorithm.
    The Annals of Statistics 50, 2179-2204.
  36. Cai, T. T. & Wei, H. (2022).
    Distributed adaptive Gaussian mean estimation with unknown variance: Interactive protocols help adaptation.
    The Annals of Statistics 50, 1992-2020.
  37. Li, S., Cai, T. T., & Li, H. (2022).
    Transfer learning for high-dimensional linear regression: Prediction, estimation, and minimax optimality.
    Journal of the Royal Statistical Society, Series B 84, 149-173.
  38. Cai, T. T. & Wei, H. (2022).
    Distributed nonparametric regression: Optimal rate of convergence and cost of adaptation.
    The Annals of Statistics, 50, 698-725.
  39. Kang, H., Lee, Y., Cai, T. T., & Small, D. (2022).
    Two robust tools for inference about causal effects with invalid instruments.
    Biometrics 78, 24-34.
  40. Ma, R., Cai, T. T., & Li, H. (2022).
    Optimal estimation of simultaneous signals using absolute inner product with applications to integrative genomics.
    Statistica Sinica 32, 1027-1048.
  41. Cai, T. T. Han, R., & Zhang, A. (2022).
    On the non-asymptotic concentration of heteroskedastic wishart-type matrix.
    Electronic Journal of Probability 27, 1-40.
  42. Zhang, A., Cai, T. T., & Wu, Y. (2022).
    Heteroskedastic PCA: Algorithm, optimality, and applications.
    The Annals of Statistics 50, 53-80.

     

    2021

  43. Cai, T. T., Wang, Y., & Zhang, L. (2021).
    The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy.
    The Annals of Statistics 49, 2825-2850.
  44. Cai, T. T., Jiang, T., & Li, X. (2021).
    Asymptotic analysis for extreme eigenvalues of principal minors of random matrices.
    The Annals of Applied Probability 31, 2953-2990.
  45. Guo, Z., Renaux, C., Buhlmann, P., & Cai, T. T. (2021).
    Group inference in high dimensions with applications to hierarchical testing.
    Electronic Journal of Statistics 15, 6633-6676.
  46. Ma, R., Cai, T. T., & Li, H. (2021).
    Optimal estimation of bacterial growth rates based on permuted monotone matrix.
    Biometrika 108, 693–708.
  47. Cai, T., Cai, T. T., & Guo, Z. (2021).
    Optimal statistical inference for individualized treatment effects in high-dimensional models.
    Journal of the Royal Statistical Society, Series B 83, 669-719.
  48. Ma, R., Cai, T. T., & Li, H. (2021).
    Optimal permutation recovery in permuted monotone matrix model.
    Journal of the American Statistical Association 116, 1358-1372.
  49. Wang, S., Cai, T. T., & Li, H. (2021).
    Optimal estimation of Wasserstein distance on a tree with an application to microbiome studies.
    Journal of the American Statistical Association 116, 1237-1253.
  50. Cai, T. T. & Zhang, L. (2021).
    A convex optimization approach to high-dimensional sparse quadratic discriminant analysis.
    The Annals of Statistics 49, 1537-1568.
  51. Wang, S., Cai, T. T., & Li, H. (2021).
    Hypothesis testing for phylogenetic composition: A minimum-cost flow perspective.
    Biometrika 108, 17-36.
  52. Ma, R., Cai, T. T., & Li, H. (2021).
    Global and simultaneous testing for high-dimensional logistic regression models.
    Journal of the American Statistical Association 116, 984-998.
  53. Cai, T. T., Kim, D., Song, X., & Wang, Y. (2021).
    Optimal estimation of eigenspace of large density matrices of quantum systems based on Pauli measurements.
    Journal of Statistical Planning and Inference 213, 50-71.
  54. Cai, T. T., Li, H., & Ma, R. (2021).
    Optimal structured principal subspace estimation: Metric entropy and minimax rates.
    Journal of Machine Learning Research 22, 1-45.
  55. Cai, T. T. & Wei, H. (2021).
    Transfer learning for nonparametric classification: Minimax rate and adaptive classifier.
    The Annals of Statistics 49, 100-128.

     

    2020

  56. Xia, Y., Cai, T. T., & Sun, W. (2020).
    GAP: A general framework for information pooling in two-sample sparse inference.
    Journal of the American Statistical Association 115, 1236-1250.
  57. Cai, T. T. & Wu, Y. (2020).
    Statistical and computational limits for sparse matrix detection.
    The Annals of Statistics 48, 1593-1614.
  58. Cai, T. T., Han, X., & Pan, G. (2020).
    Limiting laws for divergent spiked eigenvalues and largest non-spiked eigenvalue of sample covariance matrices.
    The Annals of Statistics 48, 1255-1280.
  59. Cai, T. T. & Guo, Z. (2020).
    Semi-supervised inference for explained variance in high-dimensional regression and its applications.
    Journal of the Royal Statistical Society, Series B 82, 391-419.
  60. Cai, T. T., Liang, T., & Rakhlin, A. (2020).
    Weighted message passing and minimum energy flow for heterogeneous stochastic block models with side information.
    Journal of Machine Learning Research 21, 1-34.
  61. Cai, T. T., Hu, J., Li, Y., & Zheng, X. (2020).
    High-dimensional minimum variance portfolio estimation based on high-frequency data.
    The Journal of Econometrics 214, 482-494.

     

    2019

  62. Cai, T. T. (2019).
    Gaussianization Machines for non-Gaussian function estimation models.
    Statistical Science 34, 635–656.
  63. Cai, T. T., Li, H., Ma, J., & Xia, Y. (2019).
    Differential Markov random field analysis with an application to detecting differential microbial community networks.
    Biometrika 106, 401-416.
  64. Xiang, D., Zhao, S. D., & Cai, T. T. (2019).
    Signal classification for the integrative analysis of multiple sequences of multiple tests.
    Journal of the Royal Statistical Society, Series B 81, 707-734.
  65. Cai, T. T. & Zhang, L. (2019).
    High-dimensional linear discriminant analysis: Optimality, adaptive algorithm, and missing data.
    Journal of the Royal Statistical Society, Series B 81, 675-705.
  66. Zhang, A., Brown, L. D., & Cai, T. T. (2019).
    Semi-supervised inference: General theory and estimation of means.
    The Annals of Statistics, 47, 2538-2566.
  67. Guo, Z., Wang, W., Cai, T. T., & Li, H. (2019).
    Optimal estimation of genetic relatedness in high-dimensional linear models.
    Journal of the American Statistical Association 114, 358-369.
  68. Cai, T. T., Sun, W., & Wang, W. (2019).
    CARS: Covariate assisted ranking and screening for large-scale two-sample inference (with discussion).
    Journal of the Royal Statistical Society, Series B 81, 187-234.
  69. Cai, T., Cai, T. T., Liao, K., & Liu, W. (2019).
    Large-scale simultaneous testing of cross-covariance matrix with applications to PheWAS.
    Statistica Sinica 29, 983-1005.
  70. Cai, T. T., Ma, J., & Zhang, L. (2019).
    CHIME: Clustering of high-dimensional Gaussian mixtures with EM algorithm and its optimality.
    The Annals of Statistics 47, 1234-1267.

     

    2018

  71. Guo, Z., Kang, H., Cai, T. T., & Small, D. (2018).
    Testing endogeneity with high dimensional covariates.
    The Journal of Econometrics 207, 175-187.
  72. Basu, P., Cai, T. T., Das, K., & Sun, W. (2018).
    Weighted false discovery rate control in large-scale multiple testing.
    Journal of the American Statistical Association 113, 1172-1183.
  73. Guo, Z., Kang, H., Cai, T. T., & Small, D. (2018).
    Confidence intervals for causal effects with invalid instruments using two-stage hard thresholding with voting.
    Journal of the Royal Statistical Society, Series B 80, 793-815.
  74. Cai, T. T., Zhang, L., & Zhou, H. H. (2018).
    Adaptive functional linear regression via functional principal component analysis and block thresholding.
    Statistica Sinica 28, 2455-2468.
  75. Cai, T. T. & Guo, Z. (2018).
    Accuracy assessment for high-dimensional linear regression.
    The Annals of Statistics 46, 1807-1836.
  76. Xia, Y., Cai, T. T. & Li, H. (2018).
    Joint testing and false discovery rate control for high-dimensional multivariate regression.
    Biometrika 105, 249-269.
  77. Xia, Y., Cai, T., & Cai, T. T. (2018).
    Multiple testing of submatrices of a precision matrix with applications to identification of between pathway interactions.
    Journal of the American Statistical Association 113, 328-339.
  78. Cai, T. T., Guntuboyina, A., & Wei, Y. (2018).
    Adaptive estimation of planar convex sets.
    The Annals of Statistics 46, 1018-1049.
  79. Cai, T. T. & Zhang, L. (2018).
    High-dimensional Gaussian copula regression: Adaptive estimation and statistical inference.
    Statistica Sinica 28, 963-993.
  80. Xia, Y., Cai, T., & Cai, T. T. (2018).
    Two-sample tests for high-dimensional linear regression with an application to detecting interactions.
    Statistica Sinica 28, 63-92.
  81. Cai, T. T. & Zhang, A. (2018).
    Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics.
    The Annals of Statistics 46, 60-89.

     

    2017

  82. Zhao, S.D., Cai, T. T., Cappola, T.P., Margulies, K.B., & Li, H. (2017).
    Sparse simultaneous signal detection for identifying genetically controlled disease genes.
    Journal of the American Statistical Association 112, 1032-1046.
  83. Zhao, S.D., Cai, T. T., & Li, H. (2017).
    Optimal detection of weak positive latent dependence between two sequences of multiple tests.
    Journal of Multivariate Analysis 160, 169–184.
  84. Cai, T. T., Liang, T., & Rakhlin, A. (2017).
    On detection and structural reconstruction of small world random networks.
    IEEE Transactions on Network Science and Engineering 4, 165-176.
  85. Cai, T. T., Liang, T., & Rakhlin, A. (2017).
    Computational and statistical boundaries for submatrix localization in a large noisy matrix.
    The Annals of Statistics 45, 1403-1430.
  86. Cai, T. T. & Sun, W. (2017).
    Large-scale global and simultaneous inference: Estimation and testing in very high dimensions.
    Annual Review of Economics 9, 411-439.
  87. Cai, T. T. & Guo, Z. (2017).
    Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity.
    The Annals of Statistics 45, 615-646.
  88. Liao, K. P., Sparks, J. A., Hejblum, B., Kuo, I-H., Cui, J., Lahey, L., Cagan, A., Gainer, V., Liu, W., Cai, T. T., Sokolove, J., & Cai, T. (2017).
    Phenome-wide association study of autoantibodies to citrullinated and non-citrullinated epitopes in rheumatoid arthritis.
    Arthritis & Rheumatology 69, 742-749.
  89. Cai, T. T. & Tan, X. L. (2017).
    Optimal estimation of a quadratic functional under the Gaussian two-sequence model.
    Statistica Sinica 27, 879-906.
  90. Cai, T. T. (2017).
    Global testing and large-scale multiple testing for high-dimensional covariance structures.
    Annual Review of Statistics and Its Applications 4, 423–446.
  91. Cai, T. T. & Sun, W. (2017).
    Optimal screening and discovery of sparse signals with applications to multistage high-throughput studies.
    Journal of the Royal Statistical Society, Series B 79, 197–223.

     

    2016

  92. Cai, T. T., Li, X., & Ma, Z. (2016).
    Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow.
    The Annals of Statistics 44, 2221-2251.
  93. Cai, T. T. & Zhang, L. (2016).
    Discussion of “Influential Feature PCA for High Dimensional Clustering".
    The Annals of Statistics 44, 2372-2381.
  94. Cai, T., Cai, T. T., & Zhang, A. (2016).
    Structured matrix completion with applications to genomic data integration.
    Journal of the American Statistical Association 111, 621-633.
  95. Cai, T. T., Liang, T., & Rakhlin, A. (2016).
    Geometric inference for general high-dimensional linear inverse problems.
    The Annals of Statistics 44, 1536–1563.
  96. Cai, T. T. & Zhang, A. (2016).
    Minimax rate-optimal estimation of high-dimensional covariance matrices with incomplete data.
    Journal of Multivariate Analysis 150, 55-74.
  97. Cai, T. T., Eldar, Y. C., & Li, X. (2016).
    Global testing against sparse alternatives in time-frequency analysis.
    The Annals of Statistics 44, 1438–1466.
  98. Cai, T. T. & Zhou, W. (2016).
    Matrix completion via max-norm constrained optimization.
    Electronic Journal of Statistics 10, 1493-1525.
  99. Cai, T. T., Kim, D., Wang, Y., Yuan, M., & Zhou, H. (2016).
    Optimal large-scale quantum state tomography with Pauli measurements.
    The Annals of Statistics 44, 681-712.
  100. Cai, T. T., Liu, W., & Zhou, H. (2016).
    Estimating sparse precision matrix: Optimal rates of convergence and adaptive estimation.
    The Annals of Statistics 44, 455-488.
  101. Cai, T. T., Li, H., Liu, W., & Xie, J. (2016).
    Joint estimation of multiple high-dimensional precision matrices.
    Statistica Sinica 26, 445-464.
  102. Cai, T. T., Ren, Z., & Zhou, H. (2016).
    Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (with discussion).
    Electronic Journal of Statistics 10, 1-59.
    (Rejoinder)
  103. Cai, T. T. & Zhang, A. (2016).
    Inference for high-dimensional differential correlation matrices.
    Journal of Multivariate Analysis 143, 107–126.
  104. Cai, T. T. & Yuan, M. (2016).
    Minimax and adaptive estimation of covariance operator for random variables observed on a lattice graph.
    Journal of the American Statistical Association 111, 253-265.
  105. Cai, T. T. & Liu, W. (2016).
    Large-scale multiple testing of correlations.
    Journal of the American Statistical Association 111, 229-240.
  106. Kang, H., Zhang, A., Cai, T. T., & Small, D. (2016).
    Instrumental variables estimation with some invalid instruments and its application to Mendelian randomization.
    Journal of the American Statistical Association 111, 132-144.

     

    2015

  107. Cai, T. T. & Li, X. (2015).
    Robust and computationally feasible community detection in the presence of arbitrary outlier nodes.
    The Annals of Statistics 43, 1027-1059.
  108. Cai, T. T., Ma, Z., & Wu, Y. (2015).
    Optimal estimation and rank detection for sparse spiked covariance matrices.
    Probability Theory and Related Fields 161, 781-815.
  109. Cai, T. T. & Low, M. (2015).
    A framework for estimation of convex functions.
    Statistica Sinica 25, 423-456.
  110. Cai, T. T. & Zhang, A. (2015).
    ROP: Matrix recovery via rank-one projections.
    The Annals of Statistics 43, 102-138.
  111. Sun, W., Reich, B. J., Cai, T. T., Guindani, M., & Schwartzman, A. (2015).
    False discovery control in large-scale spatial multiple testing.
    Journal of the Royal Statistical Society, Series B 77, 59-83.
  112. Cai, T. T., Liang, T., & Zhou, H. (2015).
    Law of log determinant of sample covariance matrix and optimal estimation of differential entropy for high-dimensional Gaussian distributions.
    Journal of Multivariate Analysis 137, 161-172.
  113. Jeng, J., Cai, T. T., & Li, H. (2015).
    Sparse segment identifications with applications to DNA copy number variation analysis.
    In Advanced Medical Statistics , 2nd Edition, Y. Lu, J. Fang, L., Tian, & H. Jin, eds., World Scientific, New Jersey, 863-887.
  114. Xia, Y., Cai, T., & Cai, T. T. (2015).
    Testing differential networks with applications to detecting gene-by-gene interactions.
    Biometrika 102, 247-266.

     

    2014

  115. Cai, T. T., Low, M., & Ma, Z. (2014).
    Adaptive confidence bands for nonparametric regression functions.
    Journal of the American Statistical Association 109, 1054-1070.
  116. Zhao, S.D., Cai, T. T., & Li, H. (2014).
    Direct estimation of differential networks.
    Biometrika 101, 253-268.
  117. Zhao, S.D., Cai, T. T., & Li, H. (2014).
    More powerful genetic association testing via a new statistical framework for integrative genomics.
    Biometrics 70, 881-890.
  118. Cai, T. T. & Xia, Y. (2014).
    High-Dimensional Sparse MANOVA.
    Journal of Multivariate Analysis 131, 174-196.
  119. Cai, T. T. & Wu, Y. (2014).
    Optimal detection for sparse mixtures against a given null distribution.
    IEEE Transactions on Information Theory 60, 2217-2232.
  120. Cai, T. T. & Yuan, M. (2014).
    Discussion: “A Significant Test for Lasso".
    The Annals of Statistics 42, 478-482.
  121. Cai, T. T., Liu, W., & Xia, Y. (2014).
    Two-sample test of high dimensional means under dependence.
    Journal of the Royal Statistical Society, Series B 76, 349-372.
  122. Cai, T. T. & Zhang, A. (2014).
    Sparse representation of a polytope and recovery of sparse signals and low-rank matrices.
    IEEE Transactions on Information Theory 60, 122-132.

     

    2013

  123. Cai, T. T., Ma, Z., & Wu, Y. (2013).
    Sparse PCA: Optimal rates and adaptive estimation.
    The Annals of Statistics 41, 3074-3110.
  124. Cai, T. T., Low, M., & Xia, Y. (2013).
    Adaptive confidence intervals for regression functions under shape constraints.
    The Annals of Statistics 41, 722-750.
  125. Cai, T. T. & Zhou, W. (2013).
    A max-norm constrained minimization approach to 1-bit matrix completion.
    Journal of Machine Learning Research 14, 3619-3647.
  126. Cai, T. T. & Ma, Z. (2013).
    Optimal hypothesis testing for high dimensional covariance matrices.
    Bernoulli 19, 2359-2388.
  127. Cai, T. T. & Zhang, A. (2013).
    Compressed sensing and affine rank minimization under restricted isometry.
    IEEE Transactions on Signal Processing 61, 3279-3290.
  128. Cai, T. T., Fan, J., & Jiang, T. (2013).
    Distributions of angles in random packing on spheres.
    Journal of Machine Learning Research 14, 1837-1864.
  129. Cai, T. T., Liu, W., & Xia, Y. (2013).
    Two-sample covariance matrix testing and support recovery in high-dimensional and sparse settings.
    Journal of the American Statistical Association 108, 265-277.
  130. Cai, T. T. & Zhang, A. (2013).
    Sharp RIP bound for sparse signal and low-rank matrix recovery.
    Applied And Computational Harmonic Analysis 35, 74-93.
  131. Cai, T. T., Li, H., Liu, W., & Xie, J. (2013).
    Covariate adjusted precision matrix estimation with an application in genetical genomics.
    Biometrika 100, 139-156.
  132. Cai, T. T., Ma, Z., & Wu, Y. (2013).
    Recent results on sparse principle component analysis.
    IEEE 5th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 181-183.
  133. Jeng, J., Cai, T. T., & Li, H. (2013).
    Simultaneous discovery of rare and common segment variants.
    Biometrika 100, 157-172.
  134. Cai, T. T., Ren, Z., & Zhou, H. (2013).
    Optimal rates of convergence for estimating Toeplitz covariance matrices.
    Probability Theory and Related Fields 156, 101-143.

     

    2012

  135. Cai, T. T. & Zhou, H. (2012).
    Optimal rates of convergence for sparse covariance matrix estimation.
    The Annals of Statistics 40, 2389-2420.
  136. Cai, T. T., Jeng, J., & Li, H. (2012).
    Robust detection and identification of sparse segments in ultra-high dimensional data analysis.
    Journal of the Royal Statistical Society, Series B 74, 773-797.
  137. Cai, T. T. & Zhou, H. (2012).
    Minimax estimation of large covariance matrices under l1 norm (with discussion).
    Statistica Sinica 22, 1319-1378.
  138. Cai, T. T. & Yuan, M. (2012).
    Adaptive covariance matrix estimation through block thresholding.
    The Annals of Statistics 40, 2014-2042.
  139. Cai, T. T. & Yuan, M. (2012).
    Minimax and adaptive prediction for functional linear regression.
    Journal of the American Statistical Association 107, 1201-1216.
  140. Cai, T. T. & Jiang, T. (2012).
    Phase transition in limiting distributions of coherence of high-dimensional random matrices.
    Journal of Multivariate Analysis 107, 24-39.
  141. Cai, T. T. (2012).
    Minimax and adaptive inference in nonparametric function estimation.
    Statistical Science 27, 31-50.

     

    2011

  142. Cai, T. T. & Liu, W. (2011).
    A direct estimation approach to sparse linear discriminant analysis.
    Journal of the American Statistical Association 106, 1566-1577.
  143. Cai, T. T. & Yuan, M. (2011).
    Optimal estimation of the mean function based on discretely sampled functional data: Phase transition.
    The Annals of Statistics 39, 2330-2355.
  144. Cai, T. T., Jeng, J., & Jin, J. (2011).
    Optimal detection of heterogeneous and heteroscedastic mixtures.
    Journal of the Royal Statistical Society, Series B 73, 629-662.
  145. Wang, L., Brown, L.D., & Cai, T. T. (2011).
    A difference based approach to the semiparametric partial linear model.
    Electronic Journal of Statistics 5, 619-641.
  146. Cai, T. T. & Jiang, T. (2011).
    Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices.
    The Annals of Statistics 39, 1496-1525.
  147. Cai, T. T. & Wang, L. (2011).
    Orthogonal matching pursuit for sparse signal recovery with noise.
    IEEE Transactions on Information Theory 57, 4680-4688.
  148. Cai, T. T. & Liu, W. (2011).
    Adaptive thresholding for sparse covariance matrix estimation.
    Journal of the American Statistical Association 106, 672-684.
  149. Cai, T. T., Liu, W., & Luo, X. (2011).
    A constrained l1 minimization approach to sparse precision matrix estimation.
    Journal of the American Statistical Association 106, 594-607.
  150. Xie, J., Cai, T. T., Maris, J. & Li, H. (2011).
    Optimal false discovery rate control for dependent data.
    Statistics and Its Interface 4, 417-430.
  151. Xie, J., Cai, T. T., & Li, H. (2011).
    Sample size and power analysis for sparse signal recovery in genome-wide association studies.
    Biometrika 98, 273-290.
  152. Cai, T. T. & Sun, W. (2011).
    A compound decision-theoretic approach to large-scale multiple testing.
    In High-dimensional Data Analysis, pages 75–116. World Scientific.
  153. Cai, T. T. & Low, M. (2011).
    Testing composite hypotheses, Hermite polynomials, and optimal estimation of a nonsmooth functional.
    The Annals of Statistics 39, 1012-1041.

     

    2010 & Earlier

  154. Yuan, M. & Cai, T. T. (2010).
    A reproducing kernel Hilbert space approach to functional linear regression.
    The Annals of Statistics 38, 3412-3444.
  155. Cai, T. T. & Zhou, H. (2010).
    Nonparametric regression in natural exponential families.
    In Borrowing Strength: Theory Powering Applications -- A Festschrift for Lawrence D. Brown, IMS Collections Vol. 6, 199-215.
  156. Jeng, J., Cai, T. T., & Li, H. (2010).
    Optimal sparse segment identification with application in copy number variation analysis.
    Journal of the American Statistical Association 105, 1156-1166.
  157. Cai, T. T. (2010).
    Comments on "Correlated z-values and the Accuracy of Large-Scale Statistical Estimates" by Bradley Efron.
    Journal of the American Statistical Association 105, 1055-1056.
  158. Cai, T. T., Wang, L., & Xu, G. (2010).
    New bounds for restricted isometry constants.
    IEEE Transactions on Information Theory 56, 4388-4394.
  159. Cai, T. T., Zhang, C.-H., & Zhou, H. (2010).
    Optimal rates of convergence for covariance matrix estimation.
    The Annals of Statistics 38, 2118-2144.
  160. Cai, T. T. & Sun, W. (2010).
    A compound decision-theoretic approach to large-scale multiple testing.
    In High-Dimensional Data Analysis, T. T. Cai and X. Shen, eds., World Scientific, New Jersey, 75-116.
  161. Brown, L. D., Cai, T. T., & Zhou, H. (2010).
    Nonparametric regression in exponential families.
    The Annals of Statistics 38, 2005-2046.
  162. Cai, T. T., Wang, L., & Xu, G. (2010).
    Stable recovery of sparse signals and an oracle inequality.
    IEEE Transactions on Information Theory 56, 3516-3522.
  163. Cai, T. T., Munk, A., & Schmidt-Hieber, J. (2010).
    Sharp minimax estimation of the variance of Brownian motion corrupted with Gaussian noise.
    Statistica Sinica 20, 1011-1024.
  164. Brown, L. D., Cai, T. T., Zhang, R., Zhao, L., & Zhou, H. (2010).
    The root-unroot algorithm for density estimation as implemented via wavelet block thresholding.
    Probability Theory and Related Fields 146, 401-433.
  165. Cai, T. T., Wang, L., & Xu, G. (2010).
    Shifting inequality and recovery of sparse signals.
    IEEE Transactions on Signal Processing 58, 1300-1308.
  166. Cai, T. T. & Jin, J. (2010).
    Optimal rates of convergence for estimating the null and proportion of non-null effects in large-scale multiple testing.
    The Annals of Statistics 38, 100-145.
  167. Cai, T. T. & Sun, W. (2009).
    Simultaneous testing of grouped hypotheses: Finding needles in multiple haystacks.
    Journal of the American Statistical Association 104, 1467 - 1481.
  168. Cai, T. T. & Zhou, H. (2009).
    Asymptotic equivalence and adaptive estimation for robust nonparametric regression.
    The Annals of Statistics 37, 3204-3235.
  169. Cai, T. T., Xu, G., & Zhang, J. (2009).
    On recovery of sparse signals via l1 minimization.
    IEEE Transactions on Information Theory 55, 3388-3397.
  170. Sun, W. & Cai, T. T. (2009).
    Large-scale multiple testing under dependency.
    Journal of the Royal Statistical Society, Series B 71, 393-424.
  171. Cai, T. T. & Wang, H. (2009).
    Tolerance intervals for discrete distributions in exponential families.
    Statistica Sinica 19, 905-923.
  172. Cai, T. T. & Zhou, H. (2009).
    A data-driven block thresholding approach to wavelet estimation.
    The Annals of Statistics 37, 569-595.
  173. Cai, T. T., Low, M., & Zhao, L. (2009).
    Sharp adaptive estimation by a blockwise method.
    Journal of Nonparametric Statistics 21, 839-850.
  174. Cai, T. T., Levine, M., & Wang, L. (2009).
    Variance function estimation in multivariate nonparametric regression.
    Journal of Multivariate Analysis 100, 126-136.
  175. Cai, T. T. & Wang, L. (2008).
    Adaptive variance function estimation in heteroscedastic nonparametric regression.
    The Annals of Statistics 36, 2025-2054.
  176. Brown, L. D., Cai, T. T., & Zhou, H. (2008).
    Robust nonparametric estimation via wavelet median regression.
    The Annals of Statistics 36, 2055-2084.
  177. Wang, L., Brown, L. D., Cai, T. T., & Levine, M. (2008).
    Effect of mean on variance function estimation in nonparametric regression.
    The Annals of Statistics 36, 646-664.
  178. Cai, T. T. (2008).
    Discussion of "Microarrays, Empirical Bayes, and the Two-Group Model" by Bradley Efron.
    Statistical Science 23, 29-33.
  179. Cai, T. T. (2008).
    On information pooling, adaptability and superefficiency in nonparametric function estimation.
    Journal of Multivariate Analysis 99, 412-436.
  180. Sun, W. & Cai, T. T. (2007).
    Oracle and adaptive compound decision rules for false discovery rate control.
    Journal of the American Statistical Association 102, 901-912.
  181. Cai, T. T. Jin, J., & Low, M. (2007).
    Estimation and confidence sets for sparse normal mixtures.
    The Annals of Statistics 35, 2421-2449.
  182. Jin, J. & Cai, T. T. (2007).
    Estimating the null and the proportion of non-null effects in large-scale multiple comparisons.
    Journal of the American Statistical Association 102, 495-506.
  183. Cai, T. T. & Lv, J. (2007).
    Discussion of "The Dantzig Selector: Statistical estimation when p is much larger than n" by E. Candes and T. Tao.
    The Annals of Statistics 35, 2365-2369.
  184. Cai, T. T., Low, M., & Zhao, L. (2007).
    Tradeoffs between global and local risks in nonparametric function estimation.
    Bernoulli 13, 1-19.
  185. Cai, T. T. & Hall, P. (2006).
    Prediction in functional linear regression.
    The Annals of Statistics 34, 2159-2179.
  186. Cai, T. T. & Low, M. (2006).
    Optimal adaptive estimation of a quadratic functional.
    The Annals of Statistics 34, 2298-2325.
  187. Cai, T. T. & Low, M. (2006).
    Adaptive confidence balls.
    The Annals of Statistics 34, 202-228.
  188. Cai, T. T. & Low, M. (2006).
    Adaptation under probabilistic error for estimating linear functionals.
    Journal of Multivariate Analysis 97, 231-245.
  189. Cai, T. T. (2006).
    Plugin confidence intervals in discrete distributions.
    Technical Report.
  190. Cai, T. T. & Low, M. (2005).
    Non-quadratic estimators of a quadratic functional.
    The Annals of Statistics 33, 2930-2956.
  191. Cai, T. T. & Low, M. (2005).
    On adaptive estimation of linear functionals.
    The Annals of Statistics 33, 2311-2343.
  192. Brown, L.D., Cai, T. T., & DasGupta, A. (2005).
    Discussion of "fuzzy and randomized confidence intervals and p-values" by C. J. Geyer and G. D. Meeden.
    Statistical Science 20, 375-379.
  193. Cai, T. T. & Low, M. (2005).
    Nonparametric function estimation over shrinking neighborhoods: Superefficiency and adaptation.
    The Annals of Statistics 33, 184-213.
  194. Cai, T. T. & Low, M. (2005).
    Adaptive estimation of linear functionals under different performance measures.
    Bernoulli 11, 341-358.
  195. Chicken, E. & Cai, T. T. (2005).
    Block thresholding for density estimation: Local and global adaptivity.
    Journal of Multivariate Analysis 95, 76-106.
  196. Cai, T. T. (2005).
    One-sided confidence intervals in discrete distributions.
    J. Statistical Planning and Inference 131, 63-88.
  197. Cai, T. T. & Low, M. (2004).
    An adaptation theory for nonparametric confidence intervals.
    The Annals of Statistics 32, 1805-1840.
  198. Cai, T. T. & Low, M. (2004).
    Minimax estimation of linear functionals over nonconvex parameter spaces.
    The Annals of Statistics 32, 552 - 576.
  199. Cai, T. T. (2003).
    Rates of convergence and adaptation over Besov spaces under pointwise risk.
    Statistica Sinica 13, 881-902.
  200. Cai, T. T. & Low, M. (2003).
    A note on nonparametric estimation of linear functionals.
    The Annals of Statistics 31, 1140-1153.
  201. Brown, L.D., Cai, T. T., & DasGupta, A. (2003).
    Interval estimation in exponential families.
    Statistica Sinica 13, 19-49.
  202. Brown, L.D., Cai, T. T., Low, M.G., & Zhang, C. (2002).
    Asymptotic equivalence theory for nonparametric regression with random design.
    The Annals of Statistics 30, 688-707.
  203. Cai, T. T. & Low, M. (2002).
    On modulus of continuity and adaptability in nonparametric functional estimation.
    Technical Report.
  204. Cai, T. T. (2002).
    On adaptive wavelet estimation of a derivative and other related linear inverse problems.
    J. Statistical Planning and Inference 108, 329-349.
  205. Brown, L.D., Cai, T. T., & DasGupta, A. (2002).
    Confidence intervals for a binomial proportion and asymptotic expansions.
    The Annals of Statistics 30, 160-201.
  206. Cai, T. T. (2002).
    On block thresholding in wavelet regression: Adaptivity, block size, and threshold level.
    Statistica Sinica 12, 1241-1273.
  207. Brown, L.D., Cai, T. T., & DasGupta, A. (2001).
    Interval estimation for a binomial proportion (with discussion).
    Statistical Science 16, 101-133.
  208. Cai, T. T. (2001).
    Discussion on "regularization of wavelets approximations" by A. Antoniadis and J. Fan.
    Journal of the American Statistical Association 96, 960-962.
  209. Cai, T. T., Zhang, D., & Ben-Amotz, D. (2001).
    Enhanced chemical classification of Raman images using wavelet transformation.
    Applied Spectroscopy 55, 1124-1130.
  210. Cai, T. T. & Silverman, B.W. (2001).
    Incorporating information on neighboring coefficients into wavelet estimation.
    Sankhya 63, 127-148.
  211. Cai, T. T. (1999).
    Adaptive wavelet estimation: a block thresholding and oracle inequality approach.
    The Annals of Statistics 27, 898-924.
  212. Cai, T. T. & Brown, L.D. (1999).
    Wavelet estimation for samples with random uniform design.
    Statistics and Probability Letters 42, 313-321.
  213. Shyu, C-R., Cai, T. T., & Broderick, L.S. (1999).
    On archiving and retrieval of sequential images from tomographic databases in PACS.
    Proc. SPIE - the International Society for Optical Engineering 3656, 33-40.
  214. Cai, T. T. & Brown, L.D. (1998).
    Wavelet shrinkage for nonequispaced samples.
    The Annals of Statistics 26, 1783-1799.
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