Semiparametric Estimation and Inference in Causal Inference and Measurement Error Models

This dissertation research has focused on theoretical and practical developments of semiparametric modeling and statistical inference for high dimensional data and measurement error data. In causal inference framework, when evaluating the effectiveness of medical treatments or social intervention policies, the average treatment effect becomes fundamentally important. We focus on propensity score modelling in treatment effect problems and develop new robust tools to overcome the curse of dimensionality. Furthermore, estimating and testing the effect of covariates of interest while accommodating many other covariates is an important problem in many scientific practices, including but not limited to empirical economics, public health and medical research. However when the covariates of interest are measured with error, to evaluate the effect precisely, we must reduce the bias caused by measurement error and adjust for the confounding effects simultaneously. We design a general methodology for a general single index semiparametric measurement error model and for a class of Poisson models, and introduce a bias-correction approach to construct a class of locally efficient estimators. We derive the corresponding estimating procedures and examine the asymptotic properties. Extensive simulation studies have been conducted to verify the performance of our semiparametric approaches