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

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

2005-03-29

arxiv.org/abs/math/0503674v1

Annals of Statistics 2004, Vol. 32, No. 5, 2074-2097

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000012 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000000012

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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