Open Access
September, 1981 Weak Convergence and Efficient Density Estimation at a Point
A. M. Krieger, J. Pickands III
Ann. Statist. 9(5): 1066-1078 (September, 1981). DOI: 10.1214/aos/1176345586

Abstract

We consider estimators for a multivariate probability density at a point. Efficient choices require knowledge of the density and its second derivatives although these are not known. We use consistent, but not necessarily efficient, estimators for these and use them to replace the unknown values in the choices for an efficient estimator. Our second stage estimators and the unattainable efficient choices are asymptotically equivalent. This follows because we show that an entire class of estimators converges weakly to a limiting stochastic process. We find asymptotically efficient estimators of kernel type.

Citation

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A. M. Krieger. J. Pickands III. "Weak Convergence and Efficient Density Estimation at a Point." Ann. Statist. 9 (5) 1066 - 1078, September, 1981. https://doi.org/10.1214/aos/1176345586

Information

Published: September, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0478.62027
MathSciNet: MR628762
Digital Object Identifier: 10.1214/aos/1176345586

Subjects:
Primary: 60F05
Secondary: 62G05 , 62G20

Keywords: Asymptotic efficiency , asymptotic normality , ‎embedding‎ , multivariate density estimation , weak convergence

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 5 • September, 1981
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