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Pré-Publication, Document De Travail Année : 2015

Asymptotic equivalence for density estimation and Guassian white noise: an extension

Résumé

The aim of this paper is to present an extension of the well-known asymptotic equivalence between density estimation experiments and a Gaussian white noise model. Our extension consists in enlarging the nonparametric class of the admissible densities. More precisely, we propose a way to allow densities defined on any subinterval of R, and also some discontinuous or unbounded densities are considered (so long as the discontinuity and unboundedness patterns are somehow known a priori). The concept of equivalence that we shall adopt is in the sense of the Le Cam distance between statistical models. The results are constructive: all the asymptotic equivalences are established by constructing explicit Markov kernels.
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Dates et versions

hal-01132442 , version 1 (17-03-2015)
hal-01132442 , version 2 (11-03-2022)

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Ester Mariucci. Asymptotic equivalence for density estimation and Guassian white noise: an extension. 2015. ⟨hal-01132442v1⟩
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