Kernel Estimation when Density Does Not Exist

Victoria Zinde-Walsh

Cahiers de recherche from Centre interuniversitaire de recherche en économie quantitative, CIREQ

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.

Keywords: kernel estimator; generalized functions (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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