Residual-based inference for semiparametric models
Uschi (Ursula U, Mueller), Department of Statistics, Texas A&M University, USA
In this talk, I will review some joint research with Hira Koul, Anton Schick and Wolfgang Wefelmeyer on estimating the error distribution in nonparametric and semiparametric regression, with emphasis on regression models with independent errors and covariates. We will identify various regression models where the residual-based empirical distribution function allows a simple uniform expansion, which, in particular, characterizes an efficient estimator of the error distribution function. The expansion also provides the basis for constructing goodness-of-fit tests, for example, distribution free martingale-transform tests about the form of the error distribution. I will further explain how the results can be adapted to missing data scenarios. The derivation uses the "transfer principle" for obtaining limiting distributions of complete case statistics (for general missing data models) from corresponding results in the complete data model. To conclude, I will present some related research on estimating the error distribution function in single-index regression.