Estimation of the parameter of a dynamically selected population for two subclasses of the exponential family

TL;DR

This paper addresses the estimation of parameters in a dynamically selected population within an infinite sequence, focusing on unbiased estimation, risk evaluation, and real data application in non-stationary schemes.

Contribution

It introduces a novel framework for parameter estimation in dynamically selected populations and develops unbiased estimators with asymptotic analysis.

Findings

Unbiased estimators for the parameters are derived.

Asymptotic properties of the estimators are established.

The methods are demonstrated using real data.

Abstract

We introduce the problem of estimation of the parameters of a dynamically selected population in an infinite sequence of random variables and provide its application in the statistical inference based on record values from a non-stationary scheme. We develop unbiased estimation of the parameters of the dynamically selected population and evaluate the risk of the estimators. We provide comparisons with natural estimators and obtain asymptotic results. Finally, we illustrate the applicability of the results using real data.