Variable location and scale density estimation

Jones, M. C.; McKay, I. J. and Hu, T. C. (1994). Variable location and scale density estimation. Annals of the Institute of Statistical Mathematics, 46(3) pp. 521–535.

URL: http://www.springerlink.com/content/q6501883l456m6...

Abstract

Variable (bandwidth) kernel density estimation (Abramson (1982,Ann. Statist.,10, 1217–1223)) and a kernel estimator with varying locations (Samiuddin and El-Sayyad (1990,Biometrika,77, 865–874)) are complementary ideas which essentially both afford bias of orderh⁴ as the overall smoothing parameterh -> 0, sufficient differentiability of the density permitting. These ideas are put in a more general framework in this paper. This enables us to describe a variety of ways in which scale and location variation may be extended and/or combined to good theoretical effect. This particularly includes extending the basic ideas to provide new kernel estimators with bias of orderh⁶. Technical difficulties associated with potentially overly large variations are fully accounted for in our theory.

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