Asymptotically optimal estimating equation with strongly consistent solutions for longitudinal data |
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Authors: | R. M. Balan L. Dumitrescu I. Schiopu-Kratina |
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Affiliation: | (1) Department of Statistics, Manipur University, Canchipur Imphal, 795003, Manipur, India |
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Abstract: | 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*(β) as a replacement for the “true” conditional correlation matrix of the ith individual. Using the approach of [12], 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 β defined as roots of estimation equations which are martingale transforms (in particular, roots of the sequence of asymptotically optimal equations). |
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