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Regularized robust estimation in binary regression models.

Qingguo Tang1, Rohana J Karunamuni2, Boxiao Liu2

  • 1School of Economics and Management, Nanjing University of Science and Technology, Nanjing, People's Republic of China.

Journal of Applied Statistics
|June 16, 2022
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This study introduces robust parameter estimation and variable selection for grouped binary regression models using minimum-distance methods. The proposed estimators offer efficiency and robustness against outliers and model misspecification.

Keywords:
62F35Binary regressionefficiencymaximum likelihoodminimum-distance methodsrobustnessvariable selection

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Binary regression models are widely used but sensitive to outliers and model misspecification.
  • Grouped data presents unique challenges for parameter estimation and variable selection.

Purpose of the Study:

  • To develop robust parameter estimation and variable selection methods for binary regression with grouped data.
  • To propose regularized minimum-distance estimators with enhanced robustness properties.

Main Methods:

  • Utilizing minimum Hellinger and minimum symmetric chi-squared distances.
  • Developing non-penalized and penalized minimum-distance estimators.
  • Investigating asymptotic properties including consistency, asymptotic normality, and oracle properties.

Main Results:

  • The proposed estimators demonstrate efficiency and robustness against model misspecification and outliers.
  • Monte Carlo studies confirm satisfactory finite-sample performance compared to traditional likelihood estimators.
  • Real-data applications illustrate the practical utility of the developed methods.

Conclusions:

  • The minimum-distance approach provides a robust framework for parameter estimation and variable selection in grouped binary regression.
  • The proposed regularized estimators offer a valuable alternative to standard methods, especially in the presence of data imperfections.