General selection rule from a family of linear estimators

A. V. Goldenshluger; O. V. Lepski

doi:10.1137/S0040585X97985923

General selection rule from a family of linear estimators

A. V. Goldenshluger, O. V. Lepski

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In the framework of an abstract statistical model we propose a procedure for selecting an estimator from a given family of linear estimators. We derive an upper bound on the risk of the selected estimator and demonstrate how this result can be used in order to develop minimax and adaptive minimax estimators in specific nonparametric estimation problems.

Original language	English
Pages (from-to)	209-226
Number of pages	18
Journal	Theory of Probability and its Applications
Volume	57
Issue number	2
DOIs	https://doi.org/10.1137/S0040585X97985923
State	Published - 2013

Keywords

Adaptive minimax estimation
Linear estimators
Majorant
Oracle inequality
Statistical experiment

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1137/S0040585X97985923

Cite this

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abstract = "In the framework of an abstract statistical model we propose a procedure for selecting an estimator from a given family of linear estimators. We derive an upper bound on the risk of the selected estimator and demonstrate how this result can be used in order to develop minimax and adaptive minimax estimators in specific nonparametric estimation problems.",

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AB - In the framework of an abstract statistical model we propose a procedure for selecting an estimator from a given family of linear estimators. We derive an upper bound on the risk of the selected estimator and demonstrate how this result can be used in order to develop minimax and adaptive minimax estimators in specific nonparametric estimation problems.

KW - Adaptive minimax estimation

KW - Linear estimators

KW - Majorant

KW - Oracle inequality

KW - Statistical experiment

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JO - Theory of Probability and its Applications

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General selection rule from a family of linear estimators

Abstract

Keywords

ASJC Scopus subject areas

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