Statistics Papers

Document Type

Journal Article

Date of this Version

2002

Publication Source

The Annals of Statistics

Volume

30

Issue

3

Start Page

688

Last Page

707

DOI

10.1214/aos/1028674838

Abstract

This paper establishes the global asymptotic equivalence between the nonparametric regression with random design and the white noise under sharp smoothness conditions on an unknown regression or drift function. The asymptotic equivalence is established by constructing explicit equivalence mappings between the nonparametric regression and the white-noise experiments, which provide synthetic observations and synthetic asymptotic solutions from any one of the two experiments with asymptotic properties identical to the true observations and given asymptotic solutions from the other. The impact of such asymptotic equivalence results is that an investigation in one nonparametric problem automatically yields asymptotically analogous results in all other asymptotically equivalent nonparametric problems.

Keywords

asymptotic equivalence, Le Cam's distance, nonparametric regression, white-noise model

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Date Posted: 27 November 2017

This document has been peer reviewed.