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We focus on in this paper the convergence rate of the L-N estimators for the fixed effect β in Poisson-Gamma models which are typical hierarchical generalised linear models(HGLMs). Under the proper assumptions on response variables and some smoothing conditions, we obtain the strong consistency and the convergence rate of the L-N estimator based on the combination of L-N and quasi-likelihood. © 2006 Springer-Verlag Berlin Heidelberg.
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