Pointwise Improvement of Multivariate Kernel Density Estimates

Belkacem Abdous and Alain Berlinet

Journal of Multivariate Analysis, 1998, vol. 65, issue 2, 109-128

Abstract: Multivariate kernel density estimators are known to systematically deviate from the true value near critical points of the density surface. To overcome this difficulty a method based on Rao-Blackwell's theorem is proposed. Local corrections of kernel density estimators are achieved by conditioning these estimators with respect to locally sufficient statistics. The asymptotic as well as the small sample size behavior of the improved estimators are studied. Asymptotic bias and variance are investigated and weak and complete consistency are derived under mild hypothesis.

Keywords: Multivariate kernel density estimator; Rao-Blackwellization; locally sufficient statistics (search for similar items in EconPapers)
Date: 1998
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