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On Some Applications of James-Stein Shrinkage Estimation 
Organizer and Chair: Melody Ghahramani (University of Winnipeg) 
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SYED EJAZ AHMED, Brock University
Shrinkage Strategy: From the Margin to the Centre of Universe  [PDF]
 
Stein revealed the most stunning result that the classical maximum likelihood estimator is inadmissible to the suggested shrinkage estimator. Since its inception, the Stein-type shrinkage estimation strategies have received considerable attention from researchers. Modern regularization estimation strategies extend Stein's procedures powerfully. A lot of research is going on in high dimensional data, where the number of variables is greater than the observations. Interestingly, in 1995, in the newsletter of the Royal Statistical Society, Efron predicted that shrinkage and empirical Bayes methodology would be a major area of statistical research for the early 21st century. Shrinkage strategy continues to be useful tools for efficient estimation. I will give some perspectives and historical developments of shrinkage strategy and its applications in big data analytics. 
 
SHAKHAWAT HOSSAIN, University of Winnipeg
Shrinkage Estimation for Generalized Linear Mixed Models  [PDF]
 
We proposed the pretest and shrinkage estimation methods in the generalized linear mixed models when some of the regression parameters are restricted to a linear subspace. We develop the properties of the pretest and shrinkage estimators including asymptotic distributional biases and risks. We show that these estimators have a significantly higher relative efficiency than the classical estimator. We also consider the LASSO, and numerically compare its relative performance with the proposed estimators. A Monte Carlo simulation study is conducted to evaluate the performance of these estimators with respect to the classical estimators. The study shows that the proposed estimation methods are comparable to the LASSO. A real data example is applied to illustrate the practical usefulness of the proposed estimation methods. 
 
BAHADIR YÜZBAŞI, Inonu University
Pretest, Shrinkage, Positive Shrinkage Ridge Estimators in Linear Regression Models  [PDF]
 
We suggest pretest, shrinkage and positive part shrinkage estimators based on ridge estimation in the context of a linear regression model. We compare their performance with some penalty estimators namely lasso, adaptive lasso and SCAD. Monte Carlo studies are conducted to compare the relative performance of the estimators and a real data example is given to illustrate the usefulness of the suggested methods. Further, we investigate the asymptotic properties of suggested estimators.