Generalized Linear Models for the Covariance Matrix of Correlated Data
主 题: Generalized Linear Models for the Covariance Matrix of Correlated Data
报告人: Prof. Pourahmadi (Northern Illinois University)
时 间: 2007-05-24 下午 2:00 - 3:30
地 点: 理科一号楼 1490
Sparse and parsimonious models for the covariance of longitudinal, panel
and functional data are becoming increasingly important in biostatistics,
finance, data mining, etc. From the perspective of generalized linear
models (GLM) we review the pros and cons of the existing models
corresponding to (i) {the identity link} (linear covariance models), (ii)
{inverse link} (Gaussian graphical models) and (iii) {log link} (log-linear
covariance models). Two new GLMs will be introduced using
reparameterizations (links) involving the Cholesky decomposition and
partial correlations. A systematic and data-based procedure for
formulating and fitting parsimonious/sparse models which guarantees the
positive-definiteness of the covariance matrix estimate will be
presented. The procedure essentially reduces the unintuitive task of
modeling covariance matrices to that of a sequence of autoregression
models. We indicate that once a bona fide GLM framework for modeling
covariance matrices is found, its Bayesian, nonparametric and other
extensions can be developed in direct analogy with the respective
extensions of the traditional GLM for the mean vector
