Minimum Hellinger distance estimation in a two-sample semiparametric model

  • Authors:

  • Jingjing Wu;Rohana Karunamuni;Biao Zhang

  • Affiliations:

  • Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4;Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1;Department of Mathematics, University of Toledo, Toledo, OH 43606-3390, USA

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2010

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Abstract

We investigate the estimation problem of parameters in a two-sample semiparametric model. Specifically, let X"1,...,X"n be a sample from a population with distribution function G and density function g. Independent of the X"i's, let Z"1,...,Z"m be another random sample with distribution function H and density function h(x)=exp[@a+r(x)@b]g(x), where @a and @b are unknown parameters of interest and g is an unknown density. This model has wide applications in logistic discriminant analysis, case-control studies, and analysis of receiver operating characteristic curves. Furthermore, it can be considered as a biased sampling model with weight function depending on unknown parameters. In this paper, we construct minimum Hellinger distance estimators of @a and @b. The proposed estimators are chosen to minimize the Hellinger distance between a semiparametric model and a nonparametric density estimator. Theoretical properties such as the existence, strong consistency and asymptotic normality are investigated. Robustness of proposed estimators is also examined using a Monte Carlo study.