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Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities

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Kolyan Ray, Johannes Schmidt-Hieber

Original languageEnglish
Pages (from-to)2195-2208
Number of pages14
JournalAnnales de l’Institut Henri Poincaré, Probabilités et Statistiques
Volume55
Issue number4
Early online date8 Nov 2019
DOIs
Accepted/In press25 Oct 2018
E-pub ahead of print8 Nov 2019

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Abstract

It is well-known that density estimation on the unit interval is asymptotically equivalent to a Gaussian white noise experiment, provided the densities are sufficiently smooth and uniformly bounded away from zero. We show that a uniform lower bound, whose size we sharply characterize, is in general necessary for asymptotic equivalence to hold.

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