Statistical inference for a stochastic generalized logistic differential equation

TL;DR

This paper develops statistical methods to estimate parameters in a stochastic generalized logistic differential equation, demonstrating consistency and applying EM algorithms for incomplete data scenarios.

Contribution

It introduces a maximum likelihood estimation approach for key parameters and establishes their strong consistency, including an EM algorithm for incomplete data.

Findings

Estimators for growth and shape parameters are strongly consistent.

Quadratic variation is used to estimate the diffusion parameter.

The methods are validated on complete and incomplete data scenarios.

Abstract

This research aims to estimate three parameters in a stochastic generalized logistic differential equation. We assume the intrinsic growth rate and shape parameters are constant but unknown. To estimate these two parameters, we use the maximum likelihood method and establish that the estimators for these two parameters are strongly consistent. We estimate the diffusion parameter by using the quadratic variation processes. To test our results, we evaluate two data scenarios, complete and incomplete, with fixed values assigned to the three parameters. In the incomplete data scenario, we apply an Expectation Maximization algorithm.