A Note On Nonparametric Estimation of Linear Functionals
Tony Cai and Mark Low
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Abstract:
Precise asymptotic descriptions of the minimax affine risks and
bias-variance tradeoffs for estimating linear functionals are given for
a broad class of moduli.
The results are complemented by illustrative examples
including one where it is possible to construct an estimator
which is fully adaptive over a range of parameter spaces.
- Paper:
pdf file.
- Other related papers:
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. (2005).
Adaptive estimation of linear functionals under different performance measures.
Bernoulli 11, 1-18.Cai, T. & Low, M. (2005).
On adaptive estimation of linear functionals.
The Annals of Statistics 33, 2311-2343.Cai, T. & Low, M. (2006).
Adaptation under probabilistic error for estimating linear functionals.
J. Multivariate Analysis 97, 231-245.