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Improved estimators in Bell regression model with application

Solmaz Seifollahi, Hossein Bevrani, Zakariya Yahya Algamal

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 modeling 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.

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 modeling 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.
Paper Structure (13 sections, 3 theorems, 44 equations, 1 figure, 2 tables)

This paper contains 13 sections, 3 theorems, 44 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Bell regression model
  3. Suggested Estimators
  4. Restricted estimator
  5. Pretest estimator
  6. James-Stein estimator
  7. Positive James-Stein estimator
  8. Properties of Suggested Estimators
  9. Simulation Study
  10. Application to a real dataset
  11. Conclusion
  12. Proof of Theorem \ref{['thm1']}
  13. Proof of Theorem \ref{['thm2']}

Key Result

Lemma 4.1

Let $Z_1= \sqrt{n}(\hat{\boldsymbol{\beta}}^{UN}-\boldsymbol{\beta})$, $Z_2= \sqrt{n}(\hat{\boldsymbol{\beta}}^{RE}-\boldsymbol{\beta})$ and $Z_3= \sqrt{n}(\hat{\boldsymbol{\beta}}^{UN}-\hat{\boldsymbol{\beta}}^{RE})$. Under null-hypothesis in Hn and regularity conditions of MLE, when $n$ increases: where $\boldsymbol{\kappa}_0= \boldsymbol{F}^{-1} \boldsymbol{H}^T (\boldsymbol{H} \boldsymbol{F}^{

Figures (1)

  • Figure 1: The SRE of suggested estimators when $\tau \in [0, 1]$.

Theorems & Definitions (5)

  • Lemma 4.1
  • Theorem 4.1
  • proof
  • Theorem 4.2
  • proof