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Optimal ridge estimation in the restricted logistic semiparametric regression models using generalized

Mahdi Roozbeh1

  • 1Department of Statistics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.

Journal of Applied Statistics
|April 6, 2026
PubMed
Summary

A new ridge estimator for logistic semiparametric regression addresses multicollinearity, outperforming existing methods. This statistical technique improves accuracy in analyzing binary outcomes with complex variable relationships.

Keywords:
62G0862J05Generalized cross validationPrimary: 62J12Secondary: 62J07logistic semiparametric regressionmulticollinearityridge estimationstochastic linear restrictions

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Area of Science:

  • Statistics
  • Econometrics

Background:

  • Binary logistic semiparametric regression is widely used for dichotomous dependent variables.
  • Multicollinearity, high correlation among explanatory variables, inflates estimator variance in this model.

Purpose of the Study:

  • Introduce a novel stochastic restricted iterative weighted ridge estimator for logistic semiparametric regression.
  • Address the multicollinearity problem and improve estimation accuracy.

Main Methods:

  • Develop asymptotic statistical properties for the new estimator.
  • Extend generalized cross-validation (GCV) for parameter and bandwidth selection.
  • Utilize Monte-Carlo simulations and real-life data for validation.

Main Results:

  • The proposed ridge estimator demonstrates superior performance compared to existing methods.
  • Theoretical properties of the GCV mean convergence are established.
  • Empirical evidence supports the effectiveness of the new estimator.

Conclusions:

  • The novel ridge estimator effectively mitigates multicollinearity issues in logistic semiparametric regression.
  • The extended GCV provides a robust method for parameter tuning.
  • This approach offers improved analytical capabilities for binary outcome data.