Semiparametric density estimation by local L_2-fitting

Details Semiparametric density estimation by local L_2-fitting Semiparametric density estimation by local L_2-fitting

2004-06-25

arxiv.org/abs/math/0406522v1

Annals of Statistics 2004, Vol. 32, No. 3, 1162-1191

Mathematics

Statistics Theory

Scientific paper

10.1214/009053604000000319

This article examines density estimation by combining a parametric approach with a nonparametric factor. The plug-in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor. The nonparametric factor is derived by a criterion called local L_2-fitting. A class of estimators that have multiplicative adjustment is provided, including estimators proposed by several authors as special cases, and the asymptotic theories are developed. Theoretical comparison reveals that the estimators in this class are better than, or at least competitive with, the traditional kernel estimator in a broad class of densities. The asymptotically best estimator in this class can be obtained from the elegant feature of the bias function.

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