Kernel Estimation when Density Does Not Exist
AbstractNonparametric 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.
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Bibliographic InfoPaper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 09-2005.
Length: 27 pages
Date of creation: 2005
Date of revision:
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kernel estimator; generalized functions;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Zinde-Walsh, Victoria, 2002. "Asymptotic Theory For Some High Breakdown Point Estimators," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1172-1196, October.
- 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.
- Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
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