Functional Response Models and Their Applications

• Activity Number: 378
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Xin M. Tu*+
• Companies: University of Rochester
• Keywords: distribution-free ; functional response ; generalized estimating equation ; regression analysis ; second-order moments ; U-statistics

Abstract

I will discuss a new class of semiparametric (distribution-free) regression models with functional responses. This class of functional response models (FRM) generalizes the traditional regression models by defining the response variable as a function of several responses from multiple subjects. By using such multiple-subjects-based responses, the FRM addresses a fundamental flaw in existing regression models that limits their applications to modeling the mean or the first-order moment of a response variable and makes it possible to model complex higher-order moments as in many popular non- and semi-parametric approaches. For example, under FRM, we can derive regression models to perform inference for nonparametric inference, such as two-way contingency analysis and the Mann-Whitney-Wilcoxon (MWW) rank-based tests. For semiparametric regression analysis, the FRM can be used to model complex variance components such as intraclass correlation in mixed-effects models that are extremely difficult to accomplish using existing semiparametric models. For inference of FRM, we discuss a novel approach by integrating the U-statistic theory with the generalized estimating equations.