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Variable selection via penalized minimum φ-divergence estimation in logistic regression

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  • D.M. Sakate
  • D.N. Kashid

Abstract

We propose penalized minimum φ-divergence estimator for parameter estimation and variable selection in logistic regression. Using an appropriate penalty function, we show that penalized φ-divergence estimator has oracle property. With probability tending to 1, penalized φ-divergence estimator identifies the true model and estimates nonzero coefficients as efficiently as if the sparsity of the true model was known in advance. The advantage of penalized φ-divergence estimator is that it produces estimates of nonzero parameters efficiently than penalized maximum likelihood estimator when sample size is small and is equivalent to it for large one. Numerical simulations confirm our findings.

Suggested Citation

  • D.M. Sakate & D.N. Kashid, 2014. "Variable selection via penalized minimum φ-divergence estimation in logistic regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1233-1246, June.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:6:p:1233-1246
    DOI: 10.1080/02664763.2013.864262
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    1. A. Gupta & D. Kasturiratna & T. Nguyen & L. Pardo, 2006. "A New Family of BAN Estimators for Polytomous Logistic Regression Models based on ϕ- Divergence Measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(2), pages 159-176, August.
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    4. A. K. Gupta & D. Kasturiratna & T. Nguyen & L. Pardo, 2006. "A New Family of BAN Estimators for Polytomous Logistic Regression Models based on ϕ- Divergence Measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(2), pages 159-176, August.
    5. Julio Pardo & Leandro Pardo & María Pardo, 2006. "Minimum Φ-divergence estimator in logistic regression models," Statistical Papers, Springer, vol. 47(1), pages 91-108, January.
    6. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
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