Efficient Estimation in Semiparametric Models

Suny At Binghamton, Binghamton NY

Investigators

Abstract

The Principle Investigator proposes to continue his research program on efficient estimation in semiparametric models with an emphasis on non- and semiparametric regression models, on bivariate models with partial knowledge about the marginals, and on time series models. Special attention will be paid to the possibility of (efficient) root-n consistent estimation of curves such as stationary densities and conditional expectations in time series models with independent innovations. Work on regression models will focus on diagnostics and on imputing when responses are missing at random. In connection with the latter fully imputed estimators will be studied. Such estimators impute not only the missing but also the observed responses. Current work by the Principal Investigator suggests that the fully imputed estimator is typically better than the partly imputed estimator, which only imputes the missing responses. One goal of the research is to prove this conjecture and to show that fully imputed estimators can even be made to be efficient. The work on bivariate models will deal with fine-tuning results for known and equal marginals obtained so far, and on extending such results to more general models including those in which the marginal distributions are linked through a parameter. Work on two monographs, one on efficient estimation in regression models and the other on efficient estimation in time series models, is also planned. The proposed research will advance the theory of efficient estimation in semiparametric models and will provide more efficient ways of analyzing data in many concrete problems. Since semiparametric models are widespread in many fields that use statistics, the proposed research will have an impact on all these fields. For example, results on time series and Markov chain models have applications in econometrics and mathematical finance; results on bivariate models have applications in actuarial sciences and in medical research; results on imputing are useful in medical studies. The planned monographs are intended to disseminate some of the research from the proposed research to a wider audience.