Recursive parameter estimation: asymptotic expansion

Authors :: Teo Sharia
Source :: Annals of the Institute of Statistical Mathematics. 62:343-362
Publication Year :: 2008
Publisher :: Springer Science and Business Media LLC, 2008.
Abstract: We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any preliminary restrictions on the probabilistic nature of the observation process and cover a wide class of nonlinear recursive procedures. In this paper we study asymptotic behaviour of the recursive estimators. The results of the paper can be used to determine the form of a recursive procedure which is expected to have the same asymptotic properties as the corresponding non-recursive one defined as a solution of the corresponding estimating equation.<br />Comment: 30 pages with 1 postscript figure