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Optimal L1 bandwidth selection for variable kernel density estimates

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  • Berlinet, Alain
  • Biau, Gérard
  • Rouvière, Laurent

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.

Suggested Citation

  • Berlinet, Alain & Biau, Gérard & Rouvière, Laurent, 2005. "Optimal L1 bandwidth selection for variable kernel density estimates," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 116-128, September.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:2:p:116-128
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    References listed on IDEAS

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    1. Biau, Gérard & Devroye, Luc, 2003. "On the risk of estimates for block decreasing densities," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 143-165, July.
    2. Stephan R. Sain & David W. Scott, 2002. "Zero‐Bias Locally Adaptive Density Estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 441-460, September.
    3. Sain, Stephan R., 2002. "Multivariate locally adaptive density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 165-186, April.
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