On correcting for variance inflation in kernel density estimation

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Abstract

It is a simple matter to correct for the well-known variance inflation property of nonnegative kernel density estimates whereby the estimated distribution's variance exceeds that of the sample. But should we bother? Asymptotic mean integrated squared error considerations, developed here for the first time, suggest we may. However, we observe that the difference variance correction makes is, in most practical instances, negligible. Even when this is not so, exploratory conclusions would rarely be affected and, on occasions when this is not so either, variance correction can have a slight tendency to obscure potentially important features of the density. An exception to all this is estimation of the normal density for which correcting for variance inflation is certainty appropriate. This author retains a personal preference for continuing with uncorrected kernel density estimates, but the main message of the paper is the relative indifference to whether or not variance correction is employed.

References (18)

  • B. Abdous

    Strong uniform consistency of kernel probability density estimators based on sample moments

    Statist. Probab. Lett.

    (1989)
  • P. Hall et al.

    Estimation of integrated squared demsity derivatives

    Statist. Probab. Lett.

    (1987)
  • B. Abdous, Adapting the classical kernel density estimator to data. Comput. Statist. Data Anal., to...
  • B. Abdous et al.

    On the strong uniform consistency of a new kernel density estimator

    Metrika

    (1989)
  • B. Abdous and R. Theodorescu. On the L1 strong consistency of a new kernel probability density estimator. Statist....
  • Sample moments integrating normal kernel estimators of multivariate density and regression functions

    Sankhyā Ser. B

    (1983)
  • P.J. Diggle et al.

    Monte Carlo methods of inference for implicit statistical models

    J. Roy. Statist. Soc. Ser. B

    (1984)
  • B. Efron

    Bootstrap methods - another look at the jack-knife

    Ann. Statist.

    (1979)
  • M.J. Fryer

    Some errors associated with the non-parametric estimation of density functions

    J. Inst. Math. Appl.

    (1976)
There are more references available in the full text version of this article.

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