Approximate Quasi-likelihood Estimation in Models with Surrogate Predictors

Abstract We consider quasi-likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error. We review and extend four approaches to estimation in this problem, all of them based on small measurement error approximations. A taxonomy of the data sets likely to be available in measurement error studies is developed. An asymptotic theory based on this taxonomy is obtained and includes measurement error and Berkson error models as special cases.