On structural parameter estimation of the Markov Q-process

TL;DR

This paper introduces a new unbiased estimator for the structural parameter of Markov Q-processes, a class of continuous-time Markov branching processes, and analyzes its variance asymptotically.

Contribution

It proposes an unbiased Lotka-Nagaev type estimator for the structural parameter of Markov Q-processes and derives its asymptotic variance expansion.

Findings

The estimator is unbiased.

Asymptotic variance expansion is derived.

Estimator performance analyzed for large samples.

Abstract

In the paper we consider a stochastic model which called Markov Q-processes that forms a continuous-time Markov population system. Markov Q-processes are defined as stochastic Markov branching processes with trajectories continuing in the remote future. Estimation of the structural parameter of the Markov Q-process is the main goal of this paper. To estimate this parameter, an unbiased estimator of the Lotka-Nagaev type is proposed. An asymptotic expansion of the variance of this estimator is found.