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On the Restricted Almost Unbiased Ridge Estimator in Logistic Regression
Postgraduate Institute of Science, University of Peradeniya, Peradeniya, Sri Lanka
Department of Statistics and Computer Science, University of Peradeniya, Peradeniya, Sri Lanka
Department of Mathematics and Statistics, University of Jaffna, Jaffna, Sri Lanka
- 1 Postgraduate Institute of Science, University of Peradeniya, Peradeniya, Sri Lanka
- 2 Department of Statistics and Computer Science, University of Peradeniya, Peradeniya, Sri Lanka
- 3 Department of Mathematics and Statistics, University of Jaffna, Jaffna, Sri Lanka
Open Journal of Statistics·Volume 06 (2016)·Pages 1076–1084·Published 14 November 2016·DOI10.4236/ojs.2016.66087
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Abstract
In this article, the restricted almost unbiased ridge logistic estimator (RAURLE) is proposed to estimate the parameter in a logistic regression model with exact linear re-strictions when there exists multicollinearity among explanatory variables. The performance of the proposed estimator over the maximum likelihood estimator (MLE), ridge logistic estimator (RLE), almost unbiased ridge logistic estimator (AURLE), and restricted maximum likelihood estimator (RMLE) with respect to different ridge parameters is investigated through a simulation study in terms of scalar mean square error.
KeywordsMulticollinearityRidge EstimatorAlmost Unbiased Ridge Logistic EstimatorLinear RestrictionsScalar Mean Square Error
- Schaefer, R.L., Roi, L.D. and Wolfe, R.A. (1984) A Ridge Logistic Estimator. Communications in Statistics - Theory and Methods, 13, 99-113. https://doi.org/10.1080/03610928408828664
- Liu, K. (1993) A New Class of Biased Estimate in Linear Regression. Communications in Statistics -Theory and Methods, 22, 393-402. https://doi.org/10.1080/03610929308831027
- Urgan, N.N. and Tez, M. (2008) Liu Estimator in Logistic Regression When the Data Are Collinear. International Conference. “Continuous Optimization and Knowledge-Based Technologies”, 323-327.
- Mansson, G., Kibria, B.M.G. and Shukur, G. (2012) On Liu Estimators for the Logit Regression Model. The Royal Institute of Techonology, Centre of Excellence for Science and Innovation Studies (CESIS), Sweden, Paper No. 259.
- Aguilera, A.M., Escabias, M. and Valderrama, M.J. (2006) Using Principal Components for Estimating Logistic Regression with High-Dimensional Multicollinear Data. Computational Statistics & Data Analysis, 50, 1905-1924. https://doi.org/10.1016/j.csda.2005.03.011
- Nja, M.E., Ogoke, U.P. and Nduka, E.C. (2013) The Logistic Regression Model with a Modified Weight Function. Journal of Statistical and Econometric Method, 2, 161-171.
- Inan, D. and Erdogan, B.E. (2013) Liu-Type Logistic Estimator. Communications in Statistics - Simulation and Computation, 42, 1578-1586. https://doi.org/10.1080/03610918.2012.667480
- Xinfeng, C. (2015) On the Almost Unbiased Ridge and Liu Estimator in the Logistic Regression Model. International Conference on Social Science, Education Management and Sports Education, Atlantis Press, Amsterdam, 1663-1665.
- Asar, Y. (2015) Some New Methods to Solve Multicollinearity in Logistic Regression. Communications in Statistics - Simulation and Computation, Online. https://doi.org/10.1080/03610918.2015.1053925
- Duffy, D.E. and Santner, T.J. (1989) On the Small Sample Prosperities of Norm-Restricted Maximum Likelihood Estimators for Logistic Regression Models. Communications in Statistics -Theory and Methods, 18, 959-980. https://doi.org/10.1080/03610928908829944
- Asar, Y., Arashi, M. and Wu, J. (2016) Restricted Ridge Estimator in the Logistic Regression Model. Communications in Statistics - Simulation and Computation, Online. https://doi.org/10.1080/03610918.2016.1206932
- Siray, G.U., Toker, S. and Kaciranlar, S. (2015) On the Restricted Liu Estimator in Logistic Regression Model. Communications in Statistics - Simulation and Computation, 44, 217-232. https://doi.org/10.1080/03610918.2013.771742