Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernal density estimation

Authors:
Tarn Duong;Martin L. Hazelton
Affiliations:
School of Mathematics and Statistics M1019, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia;School of Mathematics and Statistics M1019, University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
Venue:
Journal of Multivariate Analysis
Year:
2005

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Abstract

Progress in selection of smoothing parameters for kernel density estimation has been much slower in the multivariate than univariate setting. Within the context of multivariate density estimation attention has focused on diagonal bandwidth matrices. However, there is evidence to suggest that the use of full (or unconstrained) bandwidth matrices can be beneficial. This paper presents some results in the asymptotic analysis of data-driven selectors of full bandwidth matrices. In particular, we give relative rates of convergence for plug-in selectors and a biased cross-validation selector.