In order to overcome multicollinearity, we propose a stochastic restricted Liu-type maximum likelihood estimator by incorporating Liu-type maximum likelihood estimator to the logistic regression model when the linear restrictions are stochastic. We also discuss the properties of the new estimator. Moreover, we give a method to choose the biasing parameter in the new estimator. Finally, a simulation study is given to show the performance of the new estimator.
Asar, Y. and Genç, A. New Shrinkage Parameters for the Liu-Type Logistic Estimators, Communication in Statistics-Simulation and Computation 45(12), (2016), 1094--1103.
sar, Y. Some New Methods to Solve Multicollinearity in Logistic Regression, Communications in Statistics-Simulation and Computation 46(4), (2017), 2576--2586.
Farebrother, R.W. Further Results on the Mean Square Error of Ridge Regression, Journal of the Royal Statistical Society B 38,(1976), 248--250.
Liu, K. A new class of biased estimate in linear regression, Communications in Statistics Theory and Method 22(2), (1993), 393--402.
Liu, K. Using Liu-type estimator to combat collinearity, Communications in Statistics Theory and Method 32(5), (2003), 1009--1020.
Saleh, A. M. E., and Kibria, B. G. Improved ridge regression estimators for the logistic regression model, Computational Statistics 28(6), (2013), 2519--2558.
Kibria, B. G., and Saleh, A. M. E. Improving the estimators of the parameters of a probit regression model: A ridge regression approach, Journal of Statistical Planning and Inference 142(6), (2012), 1421--1435.
Månsson, K., Kibria, B. G., and Shukur, G. On Liu estimators for the logit regression model, Economic Modelling 29(4), (2012), 1483--1488.
Månsson, K., Kibria, B. G., and Shukur, G. A restricted Liu estimator for binary regression models and its application to an applied demand system, Journal of Applied Statistics 43(6), (2016), 1119--1127.
McDonald, G. C., and Galarneau, D. I. A Monte Carlo evaluation of some ridge-type estimators, Journal of the American Statistical Association 70(350), (1975), 407--416.
İnan, D., and Erdoğan, B. E. Liu-type logistic estimator, Communications in Statistics-Simulation and Computation 42(7), (2013), 1578--1586.
Rao, C. R., Helge Toutenburg, S., Shalabh, and Heumann, C. Linear models and generalizations, least squares and alternatives, 3rd Edition Springer Berlin Heidelberg New York, 2008.
R Development Core Team R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, 2016.
Wu, J., and Asar, Y. On almost unbiased ridge logistic estimator for the logistic regression model, Hacettepe Journal of Mathematics and Statistics 45(3), (2016), 989--998.
Wu, J., and Asar, Y., More on the restricted Liu estimator in the logistic regression model, Communications in Statistics - Simulation and Computation 46(5), (2017), 3680--3689
Varathan, N. and Wijekoon P. Stochastic restricted maximum likelihood estimator in logistic regression model, Open Journal of Statistics 5, (2015), 837--851.
Varathan, N., and Wijekoon, P. Ridge Estimator in Logistic Regression under Stochastic Linear Restrictions, British Journal of Mathematics and Computer Science 15(3), (2016), 1.
Varathan, N., and Wijekoon, P. Logistic Liu Estimator under stochastic linear restrictions, Statistical Papers (2016), https://doi.org/10.1007/s00362-016-0856-6
Asar, Y. and Genç, A. New Shrinkage Parameters for the Liu-Type Logistic Estimators, Communication in Statistics-Simulation and Computation 45(12), (2016), 1094--1103.
sar, Y. Some New Methods to Solve Multicollinearity in Logistic Regression, Communications in Statistics-Simulation and Computation 46(4), (2017), 2576--2586.
Farebrother, R.W. Further Results on the Mean Square Error of Ridge Regression, Journal of the Royal Statistical Society B 38,(1976), 248--250.
Liu, K. A new class of biased estimate in linear regression, Communications in Statistics Theory and Method 22(2), (1993), 393--402.
Liu, K. Using Liu-type estimator to combat collinearity, Communications in Statistics Theory and Method 32(5), (2003), 1009--1020.
Saleh, A. M. E., and Kibria, B. G. Improved ridge regression estimators for the logistic regression model, Computational Statistics 28(6), (2013), 2519--2558.
Kibria, B. G., and Saleh, A. M. E. Improving the estimators of the parameters of a probit regression model: A ridge regression approach, Journal of Statistical Planning and Inference 142(6), (2012), 1421--1435.
Månsson, K., Kibria, B. G., and Shukur, G. On Liu estimators for the logit regression model, Economic Modelling 29(4), (2012), 1483--1488.
Månsson, K., Kibria, B. G., and Shukur, G. A restricted Liu estimator for binary regression models and its application to an applied demand system, Journal of Applied Statistics 43(6), (2016), 1119--1127.
McDonald, G. C., and Galarneau, D. I. A Monte Carlo evaluation of some ridge-type estimators, Journal of the American Statistical Association 70(350), (1975), 407--416.
İnan, D., and Erdoğan, B. E. Liu-type logistic estimator, Communications in Statistics-Simulation and Computation 42(7), (2013), 1578--1586.
Rao, C. R., Helge Toutenburg, S., Shalabh, and Heumann, C. Linear models and generalizations, least squares and alternatives, 3rd Edition Springer Berlin Heidelberg New York, 2008.
R Development Core Team R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, 2016.
Wu, J., and Asar, Y. On almost unbiased ridge logistic estimator for the logistic regression model, Hacettepe Journal of Mathematics and Statistics 45(3), (2016), 989--998.
Wu, J., and Asar, Y., More on the restricted Liu estimator in the logistic regression model, Communications in Statistics - Simulation and Computation 46(5), (2017), 3680--3689
Varathan, N. and Wijekoon P. Stochastic restricted maximum likelihood estimator in logistic regression model, Open Journal of Statistics 5, (2015), 837--851.
Varathan, N., and Wijekoon, P. Ridge Estimator in Logistic Regression under Stochastic Linear Restrictions, British Journal of Mathematics and Computer Science 15(3), (2016), 1.
Varathan, N., and Wijekoon, P. Logistic Liu Estimator under stochastic linear restrictions, Statistical Papers (2016), https://doi.org/10.1007/s00362-016-0856-6
Wu, J., & Asar, Y. (2019). On the stochastic restricted Liu-type maximum likelihood estimator in logistic regression model. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 643-653. https://doi.org/10.31801/cfsuasmas.456454
AMA
Wu J, Asar Y. On the stochastic restricted Liu-type maximum likelihood estimator in logistic regression model. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):643-653. doi:10.31801/cfsuasmas.456454
Chicago
Wu, Jibo, and Yasin Asar. “On the Stochastic Restricted Liu-Type Maximum Likelihood Estimator in Logistic Regression Model”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 643-53. https://doi.org/10.31801/cfsuasmas.456454.
EndNote
Wu J, Asar Y (February 1, 2019) On the stochastic restricted Liu-type maximum likelihood estimator in logistic regression model. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 643–653.
IEEE
J. Wu and Y. Asar, “On the stochastic restricted Liu-type maximum likelihood estimator in logistic regression model”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 643–653, 2019, doi: 10.31801/cfsuasmas.456454.
ISNAD
Wu, Jibo - Asar, Yasin. “On the Stochastic Restricted Liu-Type Maximum Likelihood Estimator in Logistic Regression Model”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 643-653. https://doi.org/10.31801/cfsuasmas.456454.
JAMA
Wu J, Asar Y. On the stochastic restricted Liu-type maximum likelihood estimator in logistic regression model. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:643–653.
MLA
Wu, Jibo and Yasin Asar. “On the Stochastic Restricted Liu-Type Maximum Likelihood Estimator in Logistic Regression Model”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 643-5, doi:10.31801/cfsuasmas.456454.
Vancouver
Wu J, Asar Y. On the stochastic restricted Liu-type maximum likelihood estimator in logistic regression model. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):643-5.