A powerful method to do inference in models with finitely many parametric constraints is the empirical likelihood approach. This nonparametric maximization method was originally introduced by Owen in order to construct confidence regions for the underlying parameter. In the mean time the empirical likelihood method has been shown to also result in efficient estimation and testing. Needed are generalizations of this method that allow for semiparametric constraints and allow for infinitely many (parametric or semiparametric) constraints. The investigator extends the scope of the empirical likelihood into these two directions. This research advances the theory of estimation in semiparametric models and provides new methods to efficiently analyze data in a wide array of concrete problems. In the process technical problems of independent interest such a central limit theorems for quadratic forms with increasing dimensions are solved.
Semiparametric models are widespread in many fields that use statistics. Although this research is theoretical in nature, it has a strong practical impact by providing more effective inference methods for all those fields. For example, results on time series have applications in economic forecasting and in mathematical finance; results on bivariate models have applications in actuarial sciences and in medical research. In medical research bivariate data naturally arise as pre- and post-treatment measurements. The research will provide ample opportunities to prepare graduate students for careers in both industry and academics.
