Abstract
In this article, a biased estimator is proposed to combat multi-collinearity in the logistic regression model. The proposed estimator is a general estimator which includes other biased estimators, such as the ridge estimator and the Liu estimator as special cases. Necessary and sufficient conditions for the superiority of the new biased estimator over the maximum likelihood estimator, the ridge estimator are obtained and some properties in the mean squared error sense are discussed. Furthermore, a Monte Carlo simulation study is given to illustrate some of the theoretical results.
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References
Albert, A., Anderson, J.A.: On the existence of maximum likelihood estimates in logistic regression models. Biometrika 71, 1–10 (1984)
Alkhamisi, M., Shukur, G.: Developing ridge parameters for SUR model. Communications in Statistics Theory and Methods 37, 544–564 (2008)
Hoerl, A.E., Kennard, R.W.: Ridge regression: biased estimation for non-orthogonal Problems. Technometrics 12, 55–67 (1970a)
Hoerl, A.E., Kennard, R.W.: Ridge Regression: Application to Non-orthogonal Problems. Technometrics 12, 69–82 (1970b)
Khalaf, G., Shukur, G.: Choosing ridge parameters for regression problems. Communications in Statistics- Theory and Methods 34, 1177–1182 (2005)
Kibria, B.M.G.: Performance of some new ridge regression estimators. Communications in Statistics- Theory and Methods 32, 419–435 (2003)
Liu, K.: A new class of biased estimate in linear regression. Communications in Statistics-Theory and Methods 22, 393–402 (1993)
Mansson, K., Shukur, G.: On Ridge Parameters in Logistic Regression. Communications in Statistics, Theory and Methods 40, 3366–3381 (2011)
Mansson, K.: On Ridge Estimators for the Negative Binomial Regression Model. Economic Modelling 29, 178–184 (2012)
Nyquist, H.: Restricted estimation of generalized linear models. Applied Statistics 40, 133–141 (1991)
Schaefer, R.L., Roi, L.D., Wolfe, R.A.: A ridge logistic estimator. Communications inStatistics Theory and Methods 13, 99–113 (1984)
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Huang, J. (2012). A Simulation Research on a Biased Estimator in Logistic Regression Model. In: Li, Z., Li, X., Liu, Y., Cai, Z. (eds) Computational Intelligence and Intelligent Systems. ISICA 2012. Communications in Computer and Information Science, vol 316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34289-9_43
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DOI: https://doi.org/10.1007/978-3-642-34289-9_43
Publisher Name: Springer, Berlin, Heidelberg
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