Statistics Papers

Document Type

Journal Article

Date of this Version

2004

Publication Source

The Annals of Statistics

Volume

32

Issue

5

Start Page

2074

Last Page

2097

DOI

10.1214/009053604000000012

Abstract

This paper establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models by Poissonization. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models automatically yields asymptotically analogous results in the other models.

Keywords

asymptotic equivalence, decision theory, local limit theorem, quantile transform, white noise model

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Date Posted: 27 November 2017

This document has been peer reviewed.