Improved estimators in bell regression model with application

Abstract

In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modelling count data with multiple covariates. Furthermore, we provide a detailed explanation of the asymptotic properties of the proposed estimators, including asymptotic biases and mean squared errors. To assess the performance of the estimators, we conduct numerical studies using Monte Carlo simulations and evaluate their simulated relative efficiency. The results demonstrate that the suggested estimators outperform the unrestricted estimator when prior information is taken into account. Additionally, we present an empirical application to demonstrate the practical utility of the suggested estimators.

Keywords:

• Bell regression
• Monte Carlo simulation
• relative efficiency
• James–Stein-type estimator

MSC2020 subject classifications:

• 62F12
• 62F30
• 62J07
• 62J12

Disclosure statement

No potential conflict of interest was reported by the author(s).