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From basic to reduced bias kernel density estimators: links via Taylor series approximations

Jones, M. C. and Hössjer, O. (1996). From basic to reduced bias kernel density estimators: links via Taylor series approximations. Journal of Nonparametric Statistics, 7(1) pp. 23–34.

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The transformation kernel density estimator of Ruppert and Cline (1994) achieves bias of order h4 (as the bandwidth h→0), an improvement over the order h2 bias associated with the basic kernel density estimator. Hössjer and Ruppert (1994) use Taylor series expansions to build a bridge between the two, displaying an infinite sequence of O(h4) bias estimators in the process. In this paper, we extend the work of Hössjer and Ruppert (i) by investigating three other natural Taylor series expansions, and (ii) by applying the approach to two other O(h4) bias estimators, namely the variable bandwidth and multiplicative bias correction methods. Several further infinite sequences of O(h4) bias estimators result.

Item Type: Journal Article
Copyright Holders: 1996 Taylor & Francis
ISSN: 1048-5252
Keywords: bias reduction; kernel smoothing; multiplicative bias correction; transformation kernel estimator; variable bandwidth
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 24967
Depositing User: Sarah Frain
Date Deposited: 05 May 2011 09:53
Last Modified: 24 Dec 2013 10:46
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