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Kernel Estimation when Density Does Not Exist

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  • ZINDE-WALSH, Victoria

Abstract

Nonparametric kernel estimation of density is widely used. However, many of the pointwise and global asymptotic results for the estimator are not available unless the density is contunuous and appropriately smooth; in kernel estimation for discrete-continuous cases smoothness is required for the continuous variables. Some situations of interest may not satisfy the smoothness assumptions. In this paper the asymptotic process for the kernel estimator is examined by means of the generalized functions and generalized random processes approach according to which density and its derivatives can be defined as generalized functions. The limit process for the kernel estimator of density (whether density exists or not) is characterized in terms of a generalized Gaussian process. Conditional mean and its derivatives can be expressed as values of functionals involving generalized density; this approach makes it possible to extend asymptotic results, in particular those for asymptotic bias, to models with non-smooth density.

Suggested Citation

  • ZINDE-WALSH, Victoria, 2005. "Kernel Estimation when Density Does Not Exist," Cahiers de recherche 09-2005, Centre interuniversitaire de recherche en ├ęconomie quantitative, CIREQ.
  • Handle: RePEc:mtl:montec:09-2005
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    References listed on IDEAS

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    1. Victoria Zinde-Walsh & Peter C.B. Phillips, 2003. "Fractional Brownian Motion as a Differentiable Generalized Gaussian Process," Cowles Foundation Discussion Papers 1391, Cowles Foundation for Research in Economics, Yale University.
    2. Zinde-Walsh, Victoria, 2002. "Asymptotic Theory For Some High Breakdown Point Estimators," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1172-1196, October.
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    Cited by:

    1. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.

    More about this item

    Keywords

    kernel estimator; generalized functions;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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