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Biometrika Advance Access originally published online on February 28, 2007
Biometrika 2007 94(1):119-134; doi:10.1093/biomet/asm020
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Copyright © 2007 Biometrika Trust

Articles

Constrained local likelihood estimators for semiparametric skew-normal distributions

Yanyuan Ma and Jeffrey D. Hart

Department of Statistics, Texas A&M University, College Station,Texas 77843, U.S.A.

ma{at}stat.tamu.edu

hart{at}stat.tamu.edu

Received for publication 1 June 2005. Revision received 1 August 2006.
  Abstract

A local likelihood estimator for a nonparametric nuisance function is proposed in the context of semiparametric skew-normal distributions. Constraints imposed on such functions result in a nonparametric estimator with a different target function for maximization from classical local likelihood estimators. The optimal asymptotic semiparametric efficiency bound on parameters of interest is achieved by using this estimator in conjunction with an estimating equation formed by summing efficient scores. A generalized profile likelihood approach is also proposed. This method has the advantage of providing a unique estimate in cases where an estimating equation has multiple solutions. Our nonparametric estimator of the nuisance function leads to an estimator of the semiparametric skew-normal density. Both the estimating equation and profile likelihood approaches are applicable to more general skew-symmetric distributions.

Key Words: efficient score • local estimator • profile likelihood • semiparametric model


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