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

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dc.creatorBrown, Lawrence D.
dc.creatorCarter, Andrew V.
dc.creatorLow, Mark G.
dc.creatorZhang, Cun-Hui
dc.date2005-03-29
dc.date.accessioned2026-07-07T08:06:46Z
dc.date.available2026-07-07T08:06:46Z
dc.descriptionThis 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.
dc.descriptionPublished 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.org)
dc.identifierhttps://arxiv.org/abs/math/0503674
dc.identifierhttp://arxiv.org/abs/math/0503674
dc.identifierAnnals of Statistics 2004, Vol. 32, No. 5, 2074-2097
dc.identifierdoi:10.1214/009053604000000012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130722
dc.subjectStatistics Theory
dc.subject62B15 (Primary) 62G07, 62G20 (Secondary)
dc.titleEquivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
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