Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift



The Annals of Statistics

Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift

Lawrence D. Brown, Andrew V. Carter, Mark G. Low, and Cun-Hui Zhang

Source: Ann. Statist. Volume 32, Number 5 (2004), 2074-2097.

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.

Primary Subjects: 62B15
Secondary Subjects: 62G07, 62G20
Keywords: Asymptotic equivalence; decision theory; local limit theorem; quantile transform; white noise model

Full-text: Access granted (open access)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aos/1098883782
Digital Object Identifier: doi:10.1214/009053604000000012
Mathematical Reviews number (MathSciNet): MR2102503
Zentralblatt MATH identifier: 1062.62083

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