"Everything should be made as simple as possible, but not simpler." - Albert Einstein

Seminar Announcement

Model Selection in Sampling and Generalized Kernel Smoothing

Zonglin He, STAT-PHD Candidate Prelim Exam, Colorado State University

Monday, June 27, 2011

10:00 a.m., room 006, Statistics Bldg

ABSTRACT

The seminar consists of three parts. The first part concerns model selection in sampling. We are interested in finding an efficient model selection method applied to a sample of a finite population realized from a superpopulation. We identify PRESS as efficient based on our simulation results and develop its properties theoretically. In the second part, we are interested in fitting a nonparametric regression model to data for the situation in which the covariate is an ordered categorical variable. We extend the Nadaraya-Watson estimator, which normally requires continuous covariates, to a generalized kernel estimator that allows for ordered categorical covariates. We derive the leading bias and variance terms for the generalized kernel estimator, under the assumption that the categories correspond to quantiles of an unobserved continuous latent variable. Moreover, we extend the generalized Nadaraya- Watson estimator to the class of local linear regression estimators and derive their leading bias and
variance terms as well. The third part is our future work on developing generalized product kernel smoothing, its assymptotic theories and the simulation.

Advisory Committee:

Dr. Jean Opsomer, Advisor

Dr. Jay Breidt, Committee Member
Dr. Mary Meyer, Committee Member
Dr. John Elder, Finance & Real Estate, Outside Member