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Generalized jackknifing and higher order kernels

Jones, M. C. and Foster, P. J. (1993). Generalized jackknifing and higher order kernels. Journal of Nonparametric Statistics, 3(1) pp. 81–94.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1080/10485259308832573
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Abstract

One way of improving the performance, at least in theory, of kernel estimators of curves such as probability densities, regression functions and spectral densities is to use “higher order” kernel functions. In this paper, we investigate how one might obtain higher order kernels from lower.order ones, and put forward a wide variety of existing and novel formulae under the unifying concept of generalized jackknifing (Schucany, Gray and Owen, 1971). We thus greatly expand on the approach of Schucany and Sommers (1977). Spinoffs include links with more “direct” bias correction methods, a simplified understanding of how the “optimal” polynomial kernels of, for example, Gasser, M ller and Mammitzsch (1985) relate to one another, connections with the Gaussian-based kernels of Wand and Schucany (1990), and many extensions of Terrell and Scott's (1980) method of enforcing nonnegativity in estimates based on higher order kernel ideas.

Item Type: Journal Article
Copyright Holders: 1993 Taylor & Francis Ltd.
ISSN: 1048-5252
Keywords: bias reduction; density estimation; Gaussiab-based kernels; nonparametric regression; optimal kernels; smoothing; twicing;
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 28290
Depositing User: Sarah Frain
Date Deposited: 24 Mar 2011 12:34
Last Modified: 24 Mar 2011 12:34
URI: http://oro.open.ac.uk/id/eprint/28290
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