On the stochastic restricted Liu-type maximum likelihood estimator in logistic regression model

Year 2019, Volume: 68 Issue: 1, 643 - 653, 01.02.2019

Jibo Wu Yasin Asar

https://doi.org/10.31801/cfsuasmas.456454

Cited By: 4

Abstract

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.

Keywords

Liu-type maximum likelihood estimator , stochastic restricted Liu-type maximum likelihood estimator , multicollinearity

References

• 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