Title（标题）：On Inference of PSMD Estimators of Semi/Nonparametric Conditional Moment Models

Speaker（汇报人）：Professor Xiaohong Chen, Professor Demian Pouzo Yale University University of California, Berkeley

Time（功夫）：2011年6月30日（周四）下午3:15—4:15

Place（地址）：拉斯维加斯9888新楼217教室

Abstract（提要）：In this paper, we consider estimation and inference of functionals of unknown parameters satisfying (nonlinear) semi/nonparametric conditional moment restrictions models. Such models belong to the difficult (nonlinear) ill-posed inverse problems with unknown operators, and include nonparametric quantile instrumental variables (IV), single index IV regressions and nonparametric endogenous default model as special cases. We first establish the asymptotic normality of the penalized sieve minimum distance (PSMD) estimators of any functionals that may or may not be root-n estimable. We show that the profiled optimally weighted PSMD criterion is asymptotically chi-square distributed, which provides one simple way to construct confidence sets. We also establish the validity of bootstrap based confidence sets for possibly non-optimally weighted PSMD estimators. We illustrate the general theory by constructing confidence bands for a nonparametric quantile instrumental variables Engel curve in a Monte Carlo

study and a real data application.

About the speaker（汇报人介绍）：

北京大学统计科学中心