Asymptotic theory of generalized estimating equations based on jack-knife pseudo-observations
Modeling the expectation of a response variable \(V\) conditional on a set of covariates \(Z\) is a fundamental problem in statistical practice. When both response variable and covariates are observed from an independent and identically distributed (i.i.d) sample, estimation equations can be derived to estimate the unknown parameter \(\beta\) in the conditional expectation function. In many statistical applications, the response variable may not be observable for all subjects but a related and observable i.i.d. sample is available which can be used reasonably to estimate the unconditional mean of \(V\). It was suggested that jackknife pseudo-observations defined based on estimates of the unconditional mean of \(V\) can replace values of \(V\), which may not be observable, in the estimation equation to obtain consistent, asymptotically normal estimates of \(\beta\) with a variance that could be estimated consistently by the ordinary sandwich variance estimator. In a general setting and under some general conditions, this paper established the consistency and asymptotic normality of the estimates using recent functional analytic results. It is also found that the usual sandwich variance estimator is generally inconsistent, and a modification is proposed. Applications to several problems in survival analysis with censored responses are discussed in detail.
scientific article; zbMATH DE number 6821116