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Shrinkage estimators in zero-inflated Bell regression model with application

Solmaz Seifollahi, Hossein Bevrani, Zakariya Yahya Algamal

Abstract

We propose Stein-type estimators for zero-inflated Bell regression models by incorporating information on model parameters. These estimators combine the advantages of unrestricted and restricted estimators. We derive the asymptotic distributional properties, including bias and mean squared error, for the proposed shrinkage estimators. Monte Carlo simulations demonstrate the superior performance of our shrinkage estimators across various scenarios. Furthermore, we apply the proposed estimators to analyze a real dataset, showcasing their practical utility.

Shrinkage estimators in zero-inflated Bell regression model with application

Abstract

We propose Stein-type estimators for zero-inflated Bell regression models by incorporating information on model parameters. These estimators combine the advantages of unrestricted and restricted estimators. We derive the asymptotic distributional properties, including bias and mean squared error, for the proposed shrinkage estimators. Monte Carlo simulations demonstrate the superior performance of our shrinkage estimators across various scenarios. Furthermore, we apply the proposed estimators to analyze a real dataset, showcasing their practical utility.
Paper Structure (12 sections, 5 theorems, 55 equations, 1 figure, 2 tables)

This paper contains 12 sections, 5 theorems, 55 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Zero-inflated Bell regression model
  3. Shrinkage Methods
  4. Stein-type method
  5. Preliminary Test Method
  6. Properties of Proposed Estimators
  7. Simulation Study
  8. Application to a Real Dataset
  9. Conclusion
  10. Proof of Lemma \ref{['lem1']}
  11. Proof of Theorem \ref{['thm1']}
  12. Proof of Theorem \ref{['thm2']}

Key Result

Lemma 1

Consider Hence, under the null hypothesis in Hn, regularity conditions and when $n$ increases, we have: where $\boldsymbol{J}= \boldsymbol{F}^{-1} \boldsymbol{R}^T (\boldsymbol{R} \boldsymbol{F}^{-1}\boldsymbol{R}^T)^{-1}\boldsymbol{R}$.

Figures (1)

  • Figure 1: The SRE of suggested estimators with different values of $\delta^2$.

Theorems & Definitions (10)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • proof