Optimal L1 bandwidth selection for variable kernel density estimates

Alain Berlinet, Gérard Biau and Laurent Rouvière

Statistics & Probability Letters, 2005, vol. 74, issue 2, 116-128

Abstract: It is well-established that one can improve performance of kernel density estimates by varying the bandwidth with the location and/or the sample data at hand. Our interest in this paper is in the data-based selection of a variable bandwidth within an appropriate parameterized class of functions. We present an automatic selection procedure inspired by the combinatorial tools developed in Devroye and Lugosi [2001. Combinatorial Methods in Density Estimation. Springer, New York]. It is shown that the expected L1 error of the corresponding selected estimate is up to a given constant multiple of the best possible error plus an additive term which tends to zero under mild assumptions.

Keywords: Variable; kernel; estimate; Nonparametric; estimation; Partition; Shatter; coefficient (search for similar items in EconPapers)
Date: 2005
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