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November 2019 Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities
Kolyan Ray, Johannes Schmidt-Hieber
Ann. Inst. H. Poincaré Probab. Statist. 55(4): 2195-2208 (November 2019). DOI: 10.1214/18-AIHP946

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.

Il est bien connu que l’estimation de densité sur l’intervalle $[0,1]$ est asymptotiquement équivalente à une expérience de bruit blanc, à condition que les densités soient suffisamment régulières et uniformément bornées loin de $0$. Nous montrons qu’une borne inférieure uniforme, dont on caractérise précisément la valeur, est en général nécessaire pour que cette équivalence asymptotique ait lieu.

Citation

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Kolyan Ray. Johannes Schmidt-Hieber. "Asymptotic nonequivalence of density estimation and Gaussian white noise for small densities." Ann. Inst. H. Poincaré Probab. Statist. 55 (4) 2195 - 2208, November 2019. https://doi.org/10.1214/18-AIHP946

Information

Received: 9 February 2018; Revised: 16 August 2018; Accepted: 25 October 2018; Published: November 2019
First available in Project Euclid: 8 November 2019

zbMATH: 07161502
MathSciNet: MR4029152
Digital Object Identifier: 10.1214/18-AIHP946

Subjects:
Primary: 62B15
Secondary: 62G10, 62G20

Rights: Copyright © 2019 Institut Henri Poincaré

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Vol.55 • No. 4 • November 2019
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