Minimum Profile Hellinger Distance Estimation of General Covariate Models

Abstract

Covariate models, such as polynomial regression models, generalized linear models, and heteroscedastic models, are widely used in statistical applications. The importance of such models in statistical analysis is abundantly clear by the ever-increasing rate at which articles on covariate models are appearing in the statistical literature. Because of their flexibility, covariate models are increasingly being exploited as a convenient way to model data that consist of both a response variable and one or more covariate variables that affect the outcome of the response variable. Efficient and robust estimates for broadly defined semiparametric covariate models are investigated, and for this purpose the minimum distance approach is employed. In general, minimum distance estimators are automatically robust with respect to the stability of the quantity being estimated. In particular, minimum Hellinger distance estimation for parametric models produces estimators that are asymptotically efficient at the model density and simultaneously possess excellent robustness properties. For semiparametric covariate models, the minimum Hellinger distance method is extended and a minimum profile Hellinger distance estimator is proposed. Its asymptotic properties such as consistency are studied, and its finite-sample performance and robustness are examined by using Monte Carlo simulations and three real data analyses. Additionally, a computing algorithm is developed to ease the computation of the estimator.