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New robust statistical procedures for the polytomous logistic regression models.

Elena Castilla1, Abhik Ghosh2, Nirian Martin1

  • 1Department of Statistics, Complutense University of Madrid, 28040 Madrid, Spain.

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Summary
This summary is machine-generated.

This study introduces minimum density power divergence estimators, a robust alternative to maximum likelihood for polytomous logistic regression. These new estimators and associated tests offer improved reliability in statistical inference.

Keywords:
Influence functionMinimum density power divergence estimatorsPolytomous logistic regressionRobustnessWald-type test statistics

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Maximum likelihood estimation is standard for polytomous logistic regression.
  • Likelihood-based methods can be sensitive to outliers and model misspecification.
  • Robust statistical procedures are needed for reliable inference.

Purpose of the Study:

  • To develop a robust generalization of maximum likelihood estimators for polytomous logistic regression.
  • To introduce a family of Wald-type test statistics based on these robust estimators.
  • To theoretically and empirically evaluate the robustness of the proposed methods.

Main Methods:

  • Derivation of minimum density power divergence estimators.
  • Development of Wald-type test statistics for linear hypotheses.
  • Influence function analysis for theoretical robustness assessment.
  • Simulation studies and real-life examples for empirical validation.

Main Results:

  • A new family of robust estimators (minimum density power divergence) is proposed.
  • Robust Wald-type test statistics are introduced for hypothesis testing.
  • Theoretical analysis confirms the robustness of the proposed estimators and tests.
  • Empirical studies validate the practical performance and robustness.

Conclusions:

  • Minimum density power divergence estimators provide a robust alternative for polytomous logistic regression.
  • The proposed robust methods enhance the reliability of statistical inference.
  • Data-driven selection of the tuning parameter is proposed for practical application.