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A first-order approximated jackknifed ridge estimator in binary logistic regression

Author

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  • M. Revan Özkale

    (Cukurova University)

  • Engin Arıcan

    (Cukurova University)

Abstract

The purpose of this paper is to solve the problem of multicollinearity that affects the estimation of logistic regression model by introducing first-order approximated jackknifed ridge logistic estimator which is more efficient than the first-order approximated maximum likelihood estimator and has smaller variance than the first-order approximated jackknife ridge logistic estimator. Comparisons of the first-order approximated jackknifed ridge logistic estimator to the first-order approximated maximum likelihood, first-order approximated ridge, first-order approximated r-k class and principal components logistic regression estimators according to the bias, covariance and mean square error criteria are done. Three different estimators for the ridge parameter are also proposed. A real data set is used to see the performance of the first-order approximated jackknifed ridge logistic estimator over the first-order approximated maximum likelihood, first-order approximated ridge logistic, first-order approximated r-k class and first-order approximated principal components logistic regression estimators. Finally, two simulation studies are conducted in order to show the performance of the first-order approximated jackknife ridge logistic estimator.

Suggested Citation

  • M. Revan Özkale & Engin Arıcan, 2019. "A first-order approximated jackknifed ridge estimator in binary logistic regression," Computational Statistics, Springer, vol. 34(2), pages 683-712, June.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:2:d:10.1007_s00180-018-0851-6
    DOI: 10.1007/s00180-018-0851-6
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    References listed on IDEAS

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    1. Gruber, Marvin H. J., 1991. "The efficiency of jack-knifed and usual ridge type estimators: A comparison," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 49-51, January.
    2. Nyquist, Hans, 1988. "Applications of the jackknife procedure in ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 6(2), pages 177-183, March.
    3. Aguilera, Ana M. & Escabias, Manuel & Valderrama, Mariano J., 2006. "Using principal components for estimating logistic regression with high-dimensional multicollinear data," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1905-1924, April.
    4. M. Revan Özkale & Stanley Lemeshow & Rodney Sturdivant, 2018. "Logistic regression diagnostics in ridge regression," Computational Statistics, Springer, vol. 33(2), pages 563-593, June.
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