Statistics Papers
Title
Equivalence Theory for Density Estimation, Poisson Processes and Gaussian White Noise With Drift
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
Recommended Citation
Brown, L. D., Carter, A. V., Low, M. G., & Zhang, C. (2004). Equivalence Theory for Density Estimation, Poisson Processes and Gaussian White Noise With Drift. The Annals of Statistics, 32 (5), 2074-2097. http://dx.doi.org/10.1214/009053604000000012
Date Posted: 27 November 2017
This document has been peer reviewed.