题目：Estimation of Partially Linear Regression Model under Partial Consistency Property

报告人：Professor Heng PENG(香港浸会大学教授)

Abstract

Classic linear regression models are often criticized for requiring a response surface to be linear and additive in predictors. To ameliorate this problem, partially linear model of the form Y=Xβ+g(Z) was proposed to reduced bias. The nonparametric estimation of g(Z) involves complex tuning parameter selection and suffers from numerical instability for multivariate Z. In this paper, utilizing recent theoretical results in high dimensional statistical modeling, we propose a model-free yet computationally simple approach to estimate partially linear model. Motivated by the partial consistency phenomena, we propose to estimate g(Z) in terms of incidental parameters with partitioning its support and simply using local average to estimate the response surface. Although this estimator of g(Z) is inconsistent, we show that a root n consistent estimator of β can be obtained with little cost in efficiency. Computationally this approach only involves least squares. Moreover, conditional on the β estimates, an optimal estimator of g(Z) can then be obtained. The statistical inference problem regarding β and a two-population nonparametric testing problem regarding g(Z) are considered. Our results show that the behavior of test statistics and power of the tests are satisfactory. To assess the performance of our method in comparison with other methods, three simulation studies are conducted and a real data about gender difference in salary is analyzed.

时间：2013年4月1日（周一）下午16:00开始

地点：数学系致远楼107室