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June, 1993 Density Estimation in the $L^\infty$ Norm for Dependent Data with Applications to the Gibbs Sampler
Bin Yu
Ann. Statist. 21(2): 711-735 (June, 1993). DOI: 10.1214/aos/1176349146

Abstract

This paper investigates the density estimation problem in the $L^\infty$ norm for dependent data. It is shown that the iid optimal minimax rates are also optimal for smooth classes of stationary sequences satisfying certain $\beta$-mixing (or absolutely regular) conditions. Moreover, for given $\beta$-mixing coefficients, bounds on uniform convergence rates of kernel estimators are computed in terms of the mixing coefficients. The rates and the bounds obtained are not only for estimating the density but also for its derivatives. The results are then applied to give uniform convergence rates in problems associated with the Gibbs sampler.

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Bin Yu. "Density Estimation in the $L^\infty$ Norm for Dependent Data with Applications to the Gibbs Sampler." Ann. Statist. 21 (2) 711 - 735, June, 1993. https://doi.org/10.1214/aos/1176349146

Information

Published: June, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0792.62035
MathSciNet: MR1232514
Digital Object Identifier: 10.1214/aos/1176349146

Subjects:
Primary: 62G07
Secondary: 62F12, 62M05

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 2 • June, 1993
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