Guang Cheng
Assistant Professor, Department of Statistics, Purdue University

http://www.stat.purdue.edu/~chengg/

Date: 
Thursday, April 12, 2012

Location: 
Reception at 3 p.m. in 241 B Schaeffer Hall / Talk at 3:30 p.m. in 140 Schaeffer Hall

Abstract: In this talk, we consider the joint asymptotics and inferences for the semi-nonparametric models where the Euclidean parameter q and an infinite dimensional parameter f are both of interest. Within the general partly linear framework, we derive the joint limit distribution for (q,f (z0)) even when both parameters are estimated at different convergence rates. The marginal limit distribution for the Euclidean estimate coincides with that derived in the semiparametric literature. To construct the joint confidence region, we propose the likelihood ratio testing approach that can effectively avoid estimating the asymptotic covariance. The employed regularization tool is the smoothing spline. The undersmoothing of the smoothing spline estimate is required for obtaining the valid joint inferences. The key technical tool is a concentration inequality. A by-product result is the marginal asymptotics for f  that are new even in the nonparametric literature (without q ). 

This is a joint work with Zuofeng Shang from Univ. of Notre Dame.