A review of asymptotic theory of estimating functions

TL;DR

This paper reviews the asymptotic theory of estimating functions for stochastic processes, discussing conditions for consistency, convergence, and distribution, with examples demonstrating broad applicability.

Contribution

It provides a comprehensive review of asymptotic properties of estimating functions in stochastic process models, highlighting conditions and examples.

Findings

Conditions for consistent estimators are established.

Asymptotic distributions are characterized under broad conditions.

The theory applies to many stochastic process models.

Abstract

Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic distribution are treated separately. Our conditions are not minimal, but can be verified for many interesting stochastic process models. Several examples illustrate the wide applicability of the theory and why the generality is needed.