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Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi's Pseudodistance Estimators.

María Jaenada1, Leandro Pardo1

  • 1Department of Statistics and Operation Research, Faculty of Mathematics, Complutense University of Madrid, Plaza Ciencias, 3, 28040 Madrid, Spain.

Entropy (Basel, Switzerland)
|January 21, 2022
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Summary
This summary is machine-generated.

This study extends robust Minimum Renyi's pseudodistance estimators (MRPEs) to Generalized Linear Models (GLMs). The new methods demonstrate superior robustness and performance in statistical analysis, particularly for Poisson regression models.

Keywords:
generalized linear modelindependent and nonidentically distributed observationsinfluence function for GLMsminimum Rényi’s pseudodistance estimatorspoisson regression modelrobust Wald-type test statistics for GLMs

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Area of Science:

  • Statistics
  • Robust Statistics
  • Statistical Modeling

Background:

  • Minimum Renyi's pseudodistance estimators (MRPEs) offer robustness in linear regression models (LRMs).
  • Previous work established robust Wald-type test statistics in LRMs using MRPEs.
  • Generalizing these robust methods to broader statistical models is a key research area.

Purpose of the Study:

  • To extend Minimum Renyi's pseudodistance estimators (MRPEs) to Generalized Linear Models (GLMs) with independent and non-identically distributed observations (INIDO).
  • To develop and analyze robust Wald-type test statistics for hypothesis testing within GLMs.
  • To evaluate the robustness and performance of the proposed estimators and tests.

Main Methods:

  • Derivation of asymptotic properties for MRPEs in GLMs.
  • Analysis of the influence function for proposed MRPEs to assess robustness.
  • Definition and theoretical study of robust Wald-type test statistics, including their asymptotic distribution and influence function.
  • Empirical examination using simulation studies on Poisson Regression models.
  • Application to a real-world epilepsy treatment dataset.

Main Results:

  • The proposed MRPEs exhibit desirable robustness properties for GLMs.
  • The derived robust Wald-type test statistics are effective for linear hypothesis testing.
  • Simulation studies confirm the superior robustness of the proposed methods compared to standard approaches.
  • The methods showed practical utility in analyzing a real dataset on epilepsy treatment.

Conclusions:

  • The extension of MRPEs to GLMs provides a robust statistical framework.
  • The developed robust Wald-type tests offer reliable hypothesis testing in complex models.
  • These robust methods are valuable for statistical modeling, especially when dealing with potential outliers or model misspecification.
  • The findings have implications for statistical inference in various scientific fields, including medical research.