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Local and variable bandwidths and local linear regression

Jones, M. C. (1995). Local and variable bandwidths and local linear regression. Statistics: A journal of Theoretical and Applied Statistics, 27(1-2) pp. 65–71.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1080/02331889508802511
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Abstract

Two types of non-global bandwidth, which may be called local and variable, have been defined in attempts to improve the performance of kernel density estimators. In nonparametric regression, local linear fitting has become a method of much popularity. It is natural, therefore, to consider the use of non-global bandwidths in the local linear context, and indeed local bandwidths are often used. In this paper, it is observed that a natural proposal in the literature for combining variable, bandwidths with local linear fitting fails in the sense that the resulting mean squared error properties are those normally associated with local rather than variable bandwidths. We are able to understand why this happens in terms of weightings that are involved. We also attempt to investigate how the bias reduction expected of well-chosen variable bandwidths might be achieved in conjunction with local linear fitting.

Item Type: Journal Article
Copyright Holders: 1995 Taylor & Francis
ISSN: 1029-4910
Keywords: bias reduction; kernel smoothing; local polynomial fitting; variable kernels
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 28206
Depositing User: Sarah Frain
Date Deposited: 19 Apr 2011 14:19
Last Modified: 19 Apr 2011 14:19
URI: http://oro.open.ac.uk/id/eprint/28206
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