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Cai, T. Tony; Low, Mark G.

Adaptation under probabilistic error for estimating linear functionals. (English) Zbl 1078.62105

J. Multivariate Anal. 97, No. 1, 231-245 (2006).
Summary: The problem of estimating linear functionals based on Gaussian observations is considered. Probabilistic error is used as a measure of accuracy and attention is focused on the construction of adaptive estimators which are simultaneously near optimal under probabilistic errors over a collection of convex parameter spaces. In contrast to mean squared errors it is shown that fully rate optimal adaptive estimators can be constructed for probabilistic errors. A general construction of such estimators is provided and examples are given to illustrate the general theory.

Cited in 3 Documents

MSC:

62M99 Inference from stochastic processes
62G05 Nonparametric estimation
62G99 Nonparametric inference
62F35 Robustness and adaptive procedures (parametric inference)
62G15 Nonparametric tolerance and confidence regions

Keywords:

Adaptive estimation; Confidence intervals; Gaussian models; Modulus of continuity; Probabilistic error
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References:

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