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Estimation of integrated squared density derivatives

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  • Hall, Peter
  • Marron, J. S.
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    Abstract

    Kernel density estimators are used for the estimation of integrals of various squared derivatives of a probability density. Rates of convergence in mean squared error are calculated, which show that appropriate values of the smoothing parameter are much smaller than those for ordinary density estimation. The rate of convergence increases with stronger smoothness assumptions, however, unlike ordinary density estimation, the parametric rate of n-1 can be achieved even when only a finite amount of differentiability is assumed. The implications for data-driven bandwidth selection in ordinary density estimation are considered.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 6 (1987)
    Issue (Month): 2 (November)
    Pages: 109-115

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    Handle: RePEc:eee:stapro:v:6:y:1987:i:2:p:109-115

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    Related research

    Keywords: integrated squared derivative kernel estimators nonparametric estimation rates of convergence;

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