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2010 Multidimensional Nonparametric Density Estimates: Minimax Risk with Random Normalizing Factor
Armel Fabrice Yodeé
Afr. Diaspora J. Math. (N.S.) 10(2): 27-57 (2010).

Abstract

We consider nonparametric minimax problem of multidimensional density estimation. Using the concept of random normalizing factor, by considering the plausible hypothesis of independence, we improve the accuracy of minimax estimation $n^{-\frac{\beta}{2\beta+d}}$: with prescribed confidence level $\alpha_{n}$, we show that the best possible attainable (random) rate is $\displaystyle{\big\{\sqrt{\log(2/\alpha_{n})}/n\big\}^{\frac{2\beta}{4\beta+d}}}$. We construct an optimal estimator and an optimal random normalizing factor in the sense of Lepski.

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Armel Fabrice Yodeé. "Multidimensional Nonparametric Density Estimates: Minimax Risk with Random Normalizing Factor." Afr. Diaspora J. Math. (N.S.) 10 (2) 27 - 57, 2010.

Information

Published: 2010
First available in Project Euclid: 29 November 2010

zbMATH: 1237.62045
MathSciNet: MR2774256

Subjects:
Primary: 62G07
Secondary: 62G10 , 62G15 , 62G20

Keywords: adaptive estimation , minimax theory , nonparametric estimation , probability density model , probability density model, independence hypothese testing , random normalizing factor

Rights: Copyright © 2010 Mathematical Research Publishers

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Vol.10 • No. 2 • 2010
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