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Simple boundary correction for kernel estimation

Jones, Chris (1993). Simple boundary correction for kernel estimation. Statistics and Computing, 3(3) pp. 135–146.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1007/BF00147776
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Abstract

If a probability density function has bounded support, kernel density estimates often overspill the boundaries and are consequently especially biased at and near these edges. In this paper, we consider the alleviation of this boundary problem. A simple unified framework is provided which covers a number of straightforward methods and allows for their comparison: generalized jackknifing generates a variety of simple boundary kernel formulae. A well-known method of Rice (1984) is a special case. A popular linear correction method is another: it has close connections with the boundary properties of local linear fitting (Fan and Gijbels, 1992). Links with the optimal boundary kernels of Müller (1991) are investigated. Novel boundary kernels involving kernel derivatives and generalized reflection arise too. In comparisons, various generalized jackknifing methods perform rather similarly, so this, together with its existing popularity, make linear correction as good a method as any. In an as yet unsuccessful attempt to improve on generalized jackknifing, a variety of alternative approaches is considered. A further contribution is to consider generalized jackknife boundary correction for density derivative estimation. En route to all this, a natural analogue of local polynomial regression for density estimation is defined and discussed.

Item Type: Journal Article
Copyright Holders: 1993 Springer
ISSN: 1573-1375
Keywords: boundary kernels; derivative estimation; generalized jackknifing; local linear regression; mean squared error; optimal kernels; reflection; renormalization
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 28288
Depositing User: Sarah Frain
Date Deposited: 18 Apr 2011 09:40
Last Modified: 18 Apr 2011 09:40
URI: http://oro.open.ac.uk/id/eprint/28288
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