Semiparametric regression with missing responses

Abstract: 

The problem of incomplete data is frequently encountered in many fields, with the health sciences and survey research being obvious examples, making the analysis of data sets with missing values an important topic. The past two decades have seen a considerable amount of literature, but for the most part the focus has been on finite-dimensional parametric models. My current research seeks to go beyond this by allowing more flexible ”semiparametric” models, and by constructing estimators that are efficient, i.e. as accurate as possible. In this talk I will focus on regression models with responses that are allowed to be missing at random. The models are semiparametric in the following sense: I assume a parametric (linear or nonlinear) model for the regression function but no parametric form for the distributions of the variables; I only assume that the errors have mean zero and are independent of the covariates. For estimating general expectations of functions of covariate and response I introduce an easy-to-implement weighted imputation estimator (adapting empirical likelihood ideas). The estimator is efficient in the sense of Hajek and Le Cam, since it uses all model information. There are many open problems and related questions, which I will also address in this talk, for example extensions to more sophisticated regression models, and estimation of densities and distribution functions.

About the speaker: Ursula Muller-Harknett is Assistant Professor at the Department of Statistics, Texas A & M University. She has a PhD and Habilitation from the University of Bremen, Germany. She is interested in statistics for regression and stochastic process models with particular focus on asymptotic efficiency, in nonparametric and semiparametric inference, stochastic resonance, and in multivariate analysis.