Fall Seminar Series - October 21, 2004
University of Minnesota
School of Statistics
College of Liberal Arts

Nonparametric Modeling and Inference Functions for Longitudinal Data

Annie Qu
Statistics Department
Oregon State University

Thursday, October 21, 2004
3:30 PM, 115 Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall

Abstract

Nonparametric smoothing methods are used to model longitudinal data, but it remains a challenge to incorporate correlation into nonparametric estimation procedures. In this paper, we propose an efficient estimation procedure for varying coefficient models for longitudinal data. The proposed procedure can easily take into account correlation within subjects and directly deal with both continuous and discrete response longitudinal data under the framework of generalized linear models. Unlike the generalized estimation equation approach, the newly proposed procedure is robust with respect to specification of the working correlation matrix. For varying-coefficient models, it is often of interest to test whether coefficient functions are time-varying or time-invariant. Existing methods have not incorporated correlation information and they lack a simple form for testing properties. We propose a unified and efficient nonparametric lack-of-fit test procedure, and further demonstrate that the resulting test statistics have an asymptotic chi-squared distribution. In addition, the goodness-of-fit test is proposed to test whether the model assumption is satisfied. The corresponding test is also useful for choosing basis functions in regression spline models. We evaluate the finite sample performance of the proposed procedures with Monte Carlo simulation studies. The proposed methodology is illustrated by an analysis of a AIDS data set.