Modified almost unbiased Liu estimator in logistic regression. (English) Zbl 1497.62201
Summary: This paper focuses on introducing a new parameter estimator to the logistic regression model when the multicollinearity presents. The proposed estimator called Modified almost unbiased logistic Liu estimator (MAULLE) is obtained by composing the Liu estimator and the almost unbiased Liu estimator. Further, conditions for the superiority of the new estimator over some existing estimators were derived with respect to mean square error (MSE) and scalar mean square error (SMSE) sense. A Monte Carlo simulation study was carried out to compare the performance of the proposed estimator with some existing estimators in the scalar mean square error sense, and a real data example was discussed to illustrate the theoretical results.
MSC:
| 62J12 | Generalized linear models (logistic models) |
| 62J07 | Ridge regression; shrinkage estimators (Lasso) |
Keywords:
logistic regression; multicollinearity; Liu estimator; modified almost unbiased logistic Liu estimator; mean square errorReferences:
| [1] | Aguilera, A. M.; Escabias, M.; Valderrama, M. J., Using principal components for estimating logistic regression with high-dimensional multicollinear data, Computational Statistics & Data Analysis, 50, 1905-24 (2006) · Zbl 1445.62190 · doi:10.1016/j.csda.2005.03.011 |
| [2] | Asar, Y.; Arashi, M.; Wu, J., Restricted ridge estimator in the logistic regression model, Communications in Statistics Simmu. Comp, 46, 8, 6538-44 (2017) · Zbl 1462.62403 · doi:10.1080/03610918.2016.1206932 |
| [3] | Asar, Y.; Erişoğlu, M.; Arashi, M., Developing a restricted two-parameter Liu-type estimator: A comparison of restricted estimators in the binary logistic regression model, Communications in Statistics - Theory and Methods, 46, 14, 6864-73 (2017) · Zbl 1369.62147 · doi:10.1080/03610926.2015.1137597 |
| [4] | Duffy, D. E.; Santner, T. J., On the small sample prosperities of norm-restricted maximum likelihood estimators for logistic regression models, Communications in Statistics - Theory and Methods, 18, 3, 959-80 (1989) · Zbl 0696.62140 · doi:10.1080/03610928908829944 |
| [5] | Farebrother, R. W., Further results on the mean square error of ridge regression, Journal of the Royal Statistical Society. Series B, Statistical Methodology, 38, 248-50 (1976) · Zbl 0344.62056 · doi:10.1111/j.2517-6161.1976.tb01588.x |
| [6] | Hoerl, A. E.; Kennard, R. W., Ridge regression: Biased estimation for nonorthogonal problems, Technometrics, 12, 1, 55-67 (1970) · Zbl 0202.17205 · doi:10.2307/1267351 |
| [7] | Inan, D.; Erdogan, B. E., Liu-Type logistic estimator, Communications in Statistics- Simulation and Computation, 42, 7, 1578-86 (2013) · Zbl 1295.62071 · doi:10.1080/03610918.2012.667480 |
| [8] | Kibria, B. M. G., Performance of some new ridge regression estimators, Communications in Statistics - Theory and Methods, 32, 419-35 (2003) · Zbl 1075.62588 · doi:10.1081/SAC-120017499 |
| [9] | Mansson, G.; Kibria, B. M. G.; Shukur, G., On Liu estimators for the logit regression model, Economic Modelling (2012) |
| [10] | McDonald, G. C.; Galarneau, D. I., A Monte Carlo evaluation of some ridge type estimators, Journal of the American Statistical Association, 70, 350, 407-16 (1975) · Zbl 0319.62049 · doi:10.2307/2285832 |
| [11] | Nagarajah, V.; Wijekoon, P., Stochastic restricted maximum likelihood estimator in logistic regression model, Open Journal of Statistics, 5, 7, 837-51 (2015) · doi:10.4236/ojs.2015.57082 |
| [12] | Nja, M. E.; Ogoke, U. P.; Nduka, E. C., The logistic regression model with a modified weight function, Journal of Statistical and Econometric Method, 2, 4, 161-71 (2013) |
| [13] | Schaefer, R. L.; Roi, L. D.; Wolfe, R. A., A ridge logistic estimator, Communications in Statistics - Theory and Methods, 13, 1, 99-113 (1984) · doi:10.1080/03610928408828664 |
| [14] | Şiray, G. U.; Toker, S.; Kaçiranlar, S., On the restricted Liu estimator in logistic regression model, Communicationsin Statistics- Simulation and Computation, 44, 1, 217-32 (2015) · Zbl 1328.62403 · doi:10.1080/03610918.2013.771742 |
| [15] | Trenkler, G.; Toutenburg, H., Mean square error matrix comparisons between biased estimators-An overview of recent results, Statistical Papers, 31, 1, 165-79 (1990) · Zbl 0703.62066 · doi:10.1007/BF02924687 |
| [16] | Varathan, N.; Wijekoon, P., On the restricted almost unbiased ridge estimator in logistic regression, Open Journal of Statistics, 6, 1076-1084 (2016) · doi:10.4236/ojs.2016.66087 |
| [17] | Varathan, N.; Wijekoon, P., Ridge estimator in Logistic Regression under stochastic linear restriction, British Journal of Mathematics & Computer Science, 15, 3, 1 (2016) · doi:10.9734/BJMCS/2016/24585 |
| [18] | Varathan, N.; Wijekoon, P., Logistic Liu Estimator under stochastic linear restrictions, Statistical Papers. Online, 60, 3, 595-612 (2016) · Zbl 1420.62319 · doi:10.1007/s00362-016-0856-6 |
| [19] | Varathan, N.; Wijekoon, P., Optimal generalized logistic estimator, Communications in Statistics-Theory and Methods, 47, 2, 463-74 (2018) · Zbl 1388.62221 · doi:10.1080/03610926.2017.1307406 |
| [20] | Varathan, N.; Wijekoon, P., Liu-Type logistic estimator under Stochastic Linear Restrictions, Ceylon Journal of Science, 47, 1, 21-34 (2018) · doi:10.4038/cjs.v47i1.7483 |
| [21] | Wu, J., Modified restricted Liu estimator in logistic regression model, Computational Statistics, 31, 4, 1557-67 (2016) · Zbl 1348.65043 · doi:10.1007/s00180-015-0609-3 |
| [22] | Wu, J.; Asar, Y., On almost unbiased ridge logistic estimator for the logistic regression model, Hacettepe Journal of Mathematics and Statistics, 45, 3, 989-98 (2016) · Zbl 1359.62299 · doi:10.15672/HJMS.20156911030 |
| [23] | Xinfeng, C., On the almost unbiased ridge and Liu estimator in the logistic regression model, International Conference on Social Science, Education Management and Sports Education, 1663-1665 (2015), Atlantis Press |
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