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arXiv · 1802.03425

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

Kolyan Ray·Johannes Schmidt-Hieber
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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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Kolyan Ray, Johannes Schmidt-Hieber. 2018-02-09. Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities. https://doi.org/10.1214/18-aihp946

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