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Robins, James; van der Vaart, Aad

Adaptive nonparametric confidence sets. (English) Zbl 1091.62039

Ann. Stat. 34, No. 1, 229-253 (2006).
Summary: We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation. Applications include the finite normal mean model, the white noise model, density estimation and regression with random design.

Cited in 47 Documents

MSC:

62G15 Nonparametric tolerance and confidence regions
62G20 Asymptotic properties of nonparametric inference
62G07 Density estimation
46N30 Applications of functional analysis in probability theory and statistics
62G08 Nonparametric regression and quantile regression

Keywords:

adaptation; white noise model; density estimation; regression; testing rate
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References:

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