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Abstract Details

Activity Number: 63
Type: Topic Contributed
Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 AM
Sponsor: ENAR
Abstract - #304131
Title: Joint Asymptotics and Inferences for Seminonparametric Models
Author(s): Zuofeng Shang and Guang Cheng*+
Companies: University of Notre Dame and Purdue University
Address: 250 N. University Street, West Lafayette, IN, 47907-2066, United States
Keywords: Joint Asymptotics ; Partly Linear Models ; Likelihood Ratio Testing ; Semiparametric Efficiency ; Smoothing Spline ; Concentration Inequality

In this talk, we consider the joint asymptotics and inferences for the semi-nonparametric models where the Euclidean parameter and an infinite dimensional parameter are both of interest. Within the general partly linear framework, we derive the joint limit distribution for the two parameters which are rescaled according to 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 the infinite dimensional parameter that are new even in the nonparametric literature.

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