Estimation in Discrete Parameter Models

TL;DR

This paper explores the asymptotic properties of estimators in discrete parameter models, which are relevant in various fields, by analyzing consistency, distribution, and efficiency aspects.

Contribution

It provides a comprehensive theoretical framework for understanding asymptotic behavior in discrete parameter estimation, an area with limited prior research.

Findings

Established conditions for estimator consistency

Derived asymptotic distribution results

Explored information inequalities and efficiency relations

Abstract

In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points. In this case, we speak of discrete parameter models. Even though the problem is quite old and has interesting connections with testing and model selection, asymptotic theory for these models has hardly ever been studied. Therefore, we discuss consistency, asymptotic distribution theory, information inequalities and their relations with efficiency and superefficiency for a general class of $m$-estimators.