Joint Asymptotics and Inferences for Partly Linear Models
April 4, 2012
3:30 p.m.
Guang Cheng
Abstract
Partly linear models provide a useful class of tools for modeling complex data by naturally incorporating a combination of linear and nonlinear effects within one framework. This talk will focus on the joint asymptotics and inferences for both Euclidean parameter and
(point-wise) smooth functional parameter that have never been addressed in the literature. Specifically, we apply the penalized least square estimation to the partly linear models, i.e., partial smoothing spline.
The joint limit distribution (with essentially different convergence
rates) for both estimates is proven to be Gaussian. The marginal limit distribution for the Euclidean estimate coincides with that derived in the literature. To make joint inferences, we propose the likelihood ratio approach that can effectively avoid estimating the asymptotic covariance.
In particular, we construct the joint confidence region for both parameters and construct confidence interval for some known smooth function of both parameters. The undersmoothing of the smoothing spline estimate is required, though. In the end, we want to point out that our results can be extended to the more general quasi-likelihood framework.