Iterative estimating equations: Linear convergence and asymptotic properties

Details Iterative estimating equations: Linear convergence and asymptotic properties Iterative estimating equations: Linear convergence and asymptotic properties

2007-12-06

arxiv.org/abs/0712.0901v1

Annals of Statistics 2007, Vol. 35, No. 5, 2233-2260

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000208 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000208

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method.

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