A Note on Extended Quasi-Likelihood

We study the method of extended quasi-likelihood estimation and inference of a variance function recently proposed by Nelder and Pregibon. The estimates are inconsistent in general, and the test levels can be biased, but in many cases such as the exponential family the inconsistency and bias will not be a major concern. Extended quasi-likelihood is compared with Carroll and Ruppert's pseudo-likelihood method, which gives consistent estimates and, when slightly modified, asymptotically unbiased tests. We quantify the notion of a problem in which the amount of statistical information is large in each unit, showing in this instance that the two estimates are closely related and may be asymptotically equivalent in many important cases. However, in some cases outside the exponential family, an asymptotic bias can persist.

Duke Scholars

Author Marie Davidian Biostatistics & Bioinformatics, Division of Biostatistics