Asymptotically optimal estimating equation with strongly consistent solutions for longitudinal data. (English) Zbl 1282.62048
Summary: In this article, we introduce a conditional marginal model for longitudinal data, in which the residuals form a martingale difference sequence. This model allows us to consider a rich class of estimating equations which contains several estimating equations proposed in the literature. A particular sequence of estimating equations in this class contains a random matrix \(R^{*}_{i-1}(\beta)\) as a replacement for the “true” conditional correlation matrix of the \(i\)th individual. Using the approach of C. C. Heyde [Quasi-likelihood and its application. A general approach to optimal parameter estimation. New York, NY: Springer (1997; Zbl 0879.62076)], we identify some sufficient conditions under which this particular sequence of equations is asymptotically optimal (in our class). In the second part of the article, we identify a second set of conditions under which we prove the existence and strong consistency of a sequence of estimators of \(\beta\) defined as roots of estimation equations which are martingale transforms (in particular, roots of the sequence of asymptotically optimal equations).
MSC:
| 62F12 | Asymptotic properties of parametric estimators |
| 62J12 | Generalized linear models (logistic models) |
Keywords:
longitudinal data; generalized estimating equation; optimal parameter estimation; strong consistencyCitations:
Zbl 0879.62076References:
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