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October 2004 Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
Lawrence D. Brown, Andrew V. Carter, Mark G. Low, Cun-Hui Zhang
Ann. Statist. 32(5): 2074-2097 (October 2004). 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.

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Lawrence D. Brown. Andrew V. Carter. Mark G. Low. Cun-Hui Zhang. "Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift." Ann. Statist. 32 (5) 2074 - 2097, October 2004. https://doi.org/10.1214/009053604000000012

Information

Published: October 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1062.62083
MathSciNet: MR2102503
Digital Object Identifier: 10.1214/009053604000000012

Subjects:
Primary: 62B15
Secondary: 62G07, 62G20

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 5 • October 2004
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