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Article Dans Une Revue Annales de l'ISUP Année : 2016

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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Citer

Ester Mariucci. Asymptotic equivalence for density estimation and Guassian white noise: an extension. Annales de l'ISUP, 2016, 60 (1-2), pp.23-34. ⟨hal-01132442v2⟩
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