Department of Statistics Seminar
North Carolina State University

presents

Dr. Kimberly Weems

National Security Agency

"An Influence Function Approach to Robustness for Poisson Mixed Models"

ABSTRACT

The generalized linear mixed model (GLMM) extends classical regression analysis to non-normal, correlated response data. Our focus is primarily on mixed Poisson regression models, a class of GLMM's which is commonly used to analyze count data that exhibit overdispersion. Because inference for these models can be computationally difficult, simplifying distributional assumptions are often made. Using an influence function approach, we examine the robustness of maximum estimates (MLE's) when a main component of the model, the mixing distribution, is misspecified. We define an influence function representing effects of infinitesimal perturbations of the mixing distribution. This enables us to compute Gateaux derivatives of functionals (estimates) under perturbations of the mixing distribution for MLE's, assuming Poisson--gamma, Poisson--inverse Gaussian, and Poisson--lognormal models. Provided the first two moments exist, these MLE's are robust in the sense that their Gateaux derivatives are bounded. Some numerical results for the Poisson-gamma model are given.

Friday, March, 30, 2001

3:35 - 4:35 pm

206 Cox Hall

Refreshments will be served on the second floor of Dabney Hall (left of Room 222) at 3:00 pm.