Statistics Seminar: Jingjing Wu (Calgary) -- An Efficient and Robust Estimation Based on Profiling

The successful application of the Hellinger distance approach to fully 
parametric models is well known. The corresponding optimal estimators, 
known as minimum Hellinger distance (MHD) estimators, are efficient 
and have excellent robustness properties (Beran, 1977). This combination 
of efficiency and robustness makes MHD estimators appealing in practice. 
However, their application to semiparametric statistical models, which 
have a nuisance parameter (typically of infinite dimension), has not 
been fully studied. In this talk, we investigate a methodology to 
extend the MHD approach to general semiparametric models. We introduce 
the profile Hellinger distance and use it to construct a minimum profile 
Hellinger distance (MPHD) estimator of the finite-dimensional parameter 
of interest. This approach is analogous in some sense to the profile 
likelihood approach. We investigate the asymptotic properties such as 
the asymptotic normality, efficiency, and adaptivity of the proposed 
estimator. We also investigate its robustness properties. We present its 
small-sample properties using a Monte Carlo study.