Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 65, Issue -, Pages 127-142Publisher
BLACKWELL PUBL LTD
DOI: 10.1111/1467-9868.00376
Keywords
conjugate gradient; generalized estimating equations; generalized method of moments; infill asymptotics; longitudinal data; quadratic inference function; quasi-likelihood
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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.
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