On Adaptive Estimation of Linear Functionals
The Annals of Statistics 33, 2311-2343, (2005).

Tony Cai and Mark Low

---

• Abstract: Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two parameter spaces in the same way that the usual modulus of continuity captures the minimax difficulty of estimation over a single parameter space. A general construction of optimally adaptive estimators based on an ordered modulus of continuity is given. The results are complemented by several illustrative examples.

• Paper: pdf file.

• Other related papers:

  Cai, T. & Low, M. (2003).
  A note on nonparametric estimation of linear functionals.
  The Annals of Statistics 31, 1140-1153.

  Cai, T. & Low, M. (2003).
  Adaptation under probabilistic error for estimating linear functionals.
  Technical Report.

  Cai, T. & Low, M. (2004).
  Minimax estimation of linear functionals over nonconvex parameter spaces.
  The Annals of Statistics 32, 552 - 576.

  Cai, T. & Low, M. (2004).
  An adaptation theory for nonparametric confidence intervals.
  The Annals of Statistics 32, 1805-1840.

  Cai, T. & Low, M. (2005).
  Adaptive estimation of linear functionals under different performance measures.
  Bernoulli 11, 1-18.