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.

DOI: https://doi.org/10.1080/10485259608832686

Abstract

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.

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