Recursive Parameter Estimation: Asymptotic expansion

TL;DR

This paper analyzes the asymptotic behavior of very general recursive parameter estimators, providing insights into their long-term properties without restrictive assumptions on the observation process.

Contribution

It introduces a broad theoretical framework for understanding the asymptotic expansion of recursive estimators in nonlinear models.

Findings

Asymptotic properties of recursive estimators are characterized.

Recursive procedures can match the asymptotic behavior of non-recursive estimators.

The results apply to a wide class of nonlinear recursive estimation methods.

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.