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New two parameter hybrid estimator for zero inflated negative binomial regression models.

Fatimah A Almulhim1, M Nagy2, Ali T Hammad3

  • 1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia.

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Summary
This summary is machine-generated.

This study introduces a new hybrid estimator to improve parameter estimation in zero-inflated negative binomial regression (ZINBR) models facing multicollinearity. The novel approach enhances stability and accuracy, outperforming traditional methods in complex data scenarios.

Keywords:
Biased estimatorCount dataKibria-Lukman estimatorLiu regression estimatorModified ridge-type estimatorMulticollinearityRidge estimatorZero-inflated negative binomial regression model

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Zero-inflated negative binomial regression (ZINBR) models are crucial for count data with overdispersion and excess zeros.
  • Multicollinearity poses a significant challenge to the stability and reliability of parameter estimation in ZINBR models using maximum likelihood estimation (MLE).

Purpose of the Study:

  • To propose and evaluate a novel two-parameter hybrid estimator designed to mitigate multicollinearity issues in ZINBR models.
  • To enhance the precision and stability of parameter estimates in ZINBR models under conditions of high predictor variable correlation.

Main Methods:

  • Development of a new two-parameter hybrid estimator combining existing biased estimation techniques.
  • Theoretical comparison with established biased estimators (Ridge, Liu, Kibria-Lukman, modified Ridge).
  • Extensive Monte Carlo simulation study to assess performance under varying multicollinearity levels, using Mean Squared Error (MSE) and Mean Absolute Error (MAE).

Main Results:

  • The proposed hybrid estimator demonstrated superior performance compared to conventional biased estimators, particularly in scenarios with high multicollinearity.
  • Simulation results indicated lower MSE and MAE for the hybrid estimator, signifying improved accuracy and stability.
  • Real-world data applications confirmed the estimator's effectiveness in producing reliable parameter estimates.

Conclusions:

  • The new two-parameter hybrid estimator represents a significant advancement for parameter estimation in ZINBR models.
  • The estimator is particularly beneficial for complex datasets characterized by multicollinearity.
  • The findings support the adoption of this hybrid estimator for more robust statistical modeling of count data.