Premium
Building adaptive estimating equations when inverse of covariance estimation is difficult
Author(s) -
Qu Annie,
Lindsay Bruce G.
Publication year - 2003
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00376
Subject(s) - covariance matrix , estimation of covariance matrices , mathematics , covariance , covariance function , weighting , estimator , estimating equations , matrix (chemical analysis) , cma es , eigenvalues and eigenvectors , mathematical optimization , statistics , medicine , materials science , physics , quantum mechanics , composite material , radiology
Summary. To construct an optimal estimating function by weighting a set of score functions, we must either know or estimate consistently the covariance matrix for the individual scores. In problems with high dimensional correlated data the estimated covariance matrix could be unreliable. The smallest eigenvalues of the covariance matrix will be the most important for weighting the estimating equations, but in high dimensions these will be poorly determined. Generalized estimating equations introduced the idea of a working correlation to minimize such problems. However, it can be difficult to specify the working correlation model correctly. We develop an adaptive estimating equation method which requires no working correlation assumptions. This methodology relies on finding a reliable approximation to the inverse of the variance matrix in the quasi‐likelihood equations. We apply a multivariate generalization of the conjugate gradient method to find estimating equations that preserve the information well at fixed low dimensions. This approach is particularly useful when the estimator of the covariance matrix is singular or close to singular, or impossible to invert owing to its large size.