Abstract
It is well known that the use of prior information in the logistic regression improves the estimates of regression coefficients when multicollinearity presents. This prior information may be in the form of exact or stochastic linear restrictions. In this article, in the presence of stochastic linear restrictions, we propose a new efficient estimator, named Stochastic restricted optimal logistic estimator for the parameters in the logistic regression models when the multicollinearity presents. Further, conditions for the superiority of the new optimal estimator over some existing estimators are derived with respect to the mean square error matrix sense. Moreover, a Monte Carlo simulation study and a real data example are provided to illustrate the performance of the proposed optimal estimator in the scalar mean square error sense.
Similar content being viewed by others
References
Aguilera AM, Escabias M, Valderrama MJ (2006) Using principal components for estimating logistic regression with high-dimensional multicollinear data. Comput. Stat. Data Anal. 50:1905–1924
Asar Y, Arashi M, Wu J (2017a) Restricted ridge estimator in the logistic regression model. Commun Stat Simul Comput 46(8):6538–6544
Asar Y, Erişoǧlu M, Arashi M (2017b) Developing a restricted two-parameter Liu-type estimator: a comparison of restricted estimators in the binary logistic regression model. Commun Stat Theory Method 46(14):6864–6873
Asar Y, Genç A (2016) New shrinkage parameters for the Liu-type logistic estimators. Commun Stat Simul Comput 45(3):1094–1103
Cox D (1958) The regression analysis of binary sequences (with discussion). J R Stat Soc B 20(2):215–242
Duffy DE, Santner TJ (1989) On the small sample prosperities of norm-restricted maximum likelihood estimators for logistic regression models. Commun Stat Theory Methods 18:959–980
Inan D, Erdogan BE (2013) Liu-type logistic estimator. Commun Stat Simul Comput 42:1578–1586
Kibria BMG (2003) Performance of some new ridge regression estimators. Commun Stat Theory Methods 32:419–435
Mansson G, Kibria BMG, 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
Mansson K, Shukur G (2011) On ridge parameters in logistic regression. Commun Stat Theory Methods 40:3366–3381
McDonald GC, Galarneau DI (1975) A Monte Carlo evaluation of some ridge type estimators. J Am Stat Assoc 70:407–416
Nagarajah V, Wijekoon P (2015) Stochastic restricted maximum likelihood estimator in logistic regression model. Open J Stat 5:837–851. https://doi.org/10.4236/ojs.2015.57082
Newhouse JP, Oman SD (1971) An evaluation of ridge estimators. RAND Corporation, Santa Monica
Nja ME, Ogoke UP, Nduka EC (2013) A new logistic ridge regression estimator using exponentiated response function. J Stat Econ Methods 2(4):161–171
Özkale MR (2015) Predictive performance of linear regression models. Stati Pap 56(2):531–67
Rao CR, Toutenburg H, Shalabh HC (2008) Linear models and generalizations. Springer, Berlin
Rao CR, Toutenburg H (1995) Linear models : least squares and alternatives, 2nd edn. Springer, New York
Schaefer RL, Roi LD, Wolfe RA (1984) A ridge logistic estimator. Commun Stat Theory Methods 13:99–113
Şiray GU, Toker S, Kaçiranlar S (2015) On the restricted Liu estimator in logistic regression model. Commun Stat Simul Comput 44:217–232
Trenkler G, Toutenburg H (1990) Mean square error matrix comparisons between biased estimators? An overview of recent results. Stat Pap 31:165–179. https://doi.org/10.1007/BF02924687
van Howelingen HC, Sauerbrei W (2013) Cross-validation, shrinkage and variable selection in linear regression revisited. Open J Stat 03(02):79–102
Varathan N, Wijekoon P (2016a) On the restricted almost unbiased ridge estimator in logistic regression. Open J Stat 6:1076–1084. https://doi.org/10.4236/ojs.2016.66087
Varathan N, Wijekoon P (2016b) Ridge estimator in logistic regression under stochastic linear restriction. Br J Math Comput Sci 15(3):1. https://doi.org/10.9734/BJMCS/2016/24585
Varathan N, Wijekoon P (2016c) Logistic Liu estimator under stochastic linear restrictions. Stat Pap. https://doi.org/10.1007/s00362-016-0856-6
Varathan N, Wijekoon P (2017) A stochastic restricted almost unbiased ridge estimator in logistic regression. Proceedings of the iPURSE, University of Peradeniya, p 36. Accessed 24 Nov 2017
Varathan N, Wijekoon P (2018a) Optimal generalized logistic estimator. Commun Stat Theory Methods 47(2):463–474
Varathan N, Wijekoon P (2018b) Liu-type logistic estimator under stochastic linear restrictions. Ceylon J Sci 47(1):21–34. https://doi.org/10.4038/cjs.v47i1.7483
Varathan N, Wijekoon P (2018c) An improved stochastic restricted almost unbiased Liu-estimator in logistic regression. J Mod Appl Stat Methods, Accepted
Wu J (2016) Modified restricted Liu estimator in logistic regression model. Comput Stat 31(4):1557–1567
Wu J, Asar Y (2016) On almost unbiased ridge logistic estimator for the logistic regression model. Hacet J Math Stat 45(3):989–998. https://doi.org/10.15672/HJMS.20156911030
Xinfeng C (2015) On the almost unbiased ridge and Liu estimator in the logistic regression model. In: International conference on social science, education management and sports education. Atlantis Press, Paris, pp 1663–1665
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Varathan, N., Wijekoon, P. Optimal stochastic restricted logistic estimator. Stat Papers 62, 985–1002 (2021). https://doi.org/10.1007/s00362-019-01121-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-019-01121-y