Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
Open Access
- 1 October 2004
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 32 (5)
- https://doi.org/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.Comment: Published at http://dx.doi.org/10.1214/009053604000000012 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.orgKeywords
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