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

02/09/2018

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by   Kolyan Ray, et al.

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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.