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Biometrika 2006 93(2):472-480; doi:10.1093/biomet/93.2.472
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© 2006 Biometrika Trust

Miscellanea

Local likelihood density estimation based on smooth truncation

Pedro Delicado

Departament d'Estadística i Investigació Operativa, Universitat Politécnica de Catalunya, 08034 Barcelona, Spain. pedro.delicado{at}upc.edu

Two existing density estimators based on local likelihood have properties that are comparable to those of local likelihood regression but they are much less used than their counterparts in regression. We consider truncation as a natural way of localising parametric density estimation. Based on this idea, a third local likelihood density estimator is introduced. Our main result establishes that the three estimators coincide when a free multiplicative constant is used as an extra local parameter.

Key Words: Local polynomial regression; Nonparametric estimation; Truncated density.

Received May 2004. Revised November 2005.


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