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December, 1976 On the Maximal Deviation of $k$-Dimensional Density Estimates
M. Rosenblatt
Ann. Probab. 4(6): 1009-1015 (December, 1976). DOI: 10.1214/aop/1176995945

Abstract

Probability density estimates are generated by a kernel or weight function. Limit theorems are obtained for the maximum of the normalized deviation of the estimate from its expected value. The results are, in part, an extension to the $k$-dimensional case $(k > 1)$ of those obtained by P. Bickel and M. Rosenblatt (Ann. Statist. 1973, 1071-1095) one dimensionally.

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M. Rosenblatt. "On the Maximal Deviation of $k$-Dimensional Density Estimates." Ann. Probab. 4 (6) 1009 - 1015, December, 1976. https://doi.org/10.1214/aop/1176995945

Information

Published: December, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0369.62028
MathSciNet: MR428580
Digital Object Identifier: 10.1214/aop/1176995945

Subjects:
Primary: 60F10
Secondary: 62G05

Keywords: $k$-dimensional density estimates , Gaussian random field , maximal deviation

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • December, 1976
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