FRIDAY, December 2, 2005
Time: 2:30 - 3:30 PM
Constant Hall Room 1065

Title: Efficient Estimating Equations for Analyzing Structured Correlation Matrices

Yihao Deng
Department of Mathematics and Statistics
Old Dominion University

Correlated data occurs naturally in many scientific investigations where observations are collected on a random sample of clusters, families, or repeated measurements are taken on sampled items or subjects. The data could be continuous or discrete. An important problem in the analysis of such data is efficient estimation of the within cluster or within subject correlation. Maximum likelihood is clearly the most efficient method if the likelihood of the data is known, and in the absence of the likelihood Godambe's optimal unbiased estimating equation is an alternative for estimating the within cluster correlation. In this talk we will first show that the ML and Godambe's methods coincide for normal data. We will then discuss classes of weighted unbiased estimating equations based on Cholesky decompositions of the inverse of the correlation matrices. In special cases, I will present closed form simplified expressions for efficiencies of these unbiased equations. In the general case, we will derive the optimal weights for common structured correlation matrices. These optimal weighted estimating equations will be useful for estimating efficiently the correlation for non-normal continuous data, with minimal assumptions. Finally, I will discuss some ongoing research on the ranges of association measures for familial binary data.