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Statistical Papers

, Volume 60, Issue 3, pp 945–962 | Cite as

Logistic Liu Estimator under stochastic linear restrictions

  • Nagarajah VarathanEmail author
  • Pushpakanthie Wijekoon
Regular Article

Abstract

In order to overcome the problem of multicollinearity in logistic regression, several researchers proposed alternative estimators when exact linear restrictions are available in addition to sample model. However, in practical situations the linear restrictions are not always exact and mostly their nature is stochastic. In this paper, we propose a new estimator called stochastic restricted Liu maximum likelihood estimator (SRLMLE) by incorporating Liu estimator to the logistic regression model when the linear restrictions are stochastic. Moreover, the conditions for superiority of SRLMLE over the maximum likelihood estimator (MLE), stochastic restricted maximum likelihood estimator (SRMLE) and restricted Liu logistic estimator (RLLE) are derived with respect to mean square error criterion. Finally, the performance of the new estimator over MLE, LLE, SRMLE and RLLE is investigated in the sense of scalar mean squared error by conducting a Monte Carlo simulation and using a numerical example.

Keywords

Logistic regression Multicollinearity Liu estimator Stochastic restricted Liu maximum likelihood estimator Stochastic linear restrictions 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Postgraduate Institute of ScienceUniversity of PeradeniyaPeradeniyaSri Lanka
  2. 2.Department of Mathematics and StatisticsUniversity of JaffnaJaffnaSri Lanka
  3. 3.Department of Statistics and Computer ScienceUniversity of PeradeniyaPeradeniyaSri Lanka

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