Nonparametric and semiparametric regression, missing data, and related algorithms

Abstract

OF THE DISSERTATION Nonparametric and Semiparametric Regression, Missing Data, and Related Algorithms by MINGYU LI Dissertation Director: Minge Xie This dissertation consists of two chapters: • Chapter 1 develops nonparametric and semiparametric regression methodologies which relate the group testing responses to the individual covariates information. In this chapter, we extend the parametric regression model of Xie (2001) for binary group testing data to the nonparametric and semiparametric models. We fit nonparametric and semiparametric models and obtain estimators of the parameters by maximizing penalized likelihood function. For implementation, we apply EM algorithm considering the individual responses as complete data and the group testing responses as observed data. Simulation studies are performed to illustrate the methodologies and to evaluate the finite sample performance of our methods. In general, group testing involves a large number of subjects, hence, the computational aspect is also discussed. The results show that our estimation methods perform well for estimating both the individual probability of positive outcome and the prevalence rate in the population. • Chapter 2 studies a partially linear regression model with missing response variable and develops semiparametric efficient inference for the parametric component