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In this talk, we consider estimation in generalized linear models when there are many potential predictors and
some of them may not have influence on the response of interest. In the context of two competing models where
one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based
on subject matter or prior knowledge, we investigate the relative performances of Stein type shrinkage, pretest,
and penalty estimators (L1GLM, adaptive L1GLM, and SCAD) with respect to the unrestricted maximum
likelihood estimator (MLE). The asymptotic properties of the pretest and shrinkage estimators including the
derivation of asymptotic distributional biases and risks are established. In particular, we give conditions under
which the shrinkage estimators are asymptotically more efficient than the unrestricted MLE. A Monte Carlo
simulation study show that the mean squared error (MSE) of an adaptive shrinkage estimator is comparable
to the MSE of the penalty estimators in many situations and in particular performs better than the penalty
estimators when the dimension of the restricted parameter space is large. The Steinian shrinkage and penalty
estimators all improve substantially on the unrestricted MLE. A real data set analysis is also presented to compare
the suggested methods.
Ejaz Ahmed is professor and Dean of Mathematics and Statistics. Before joining Brock, he was a professor and head of Mathematics
at the University of Windsor and University of Regina. Prior to that, he had a faculty position at the University of Western Ontario.
He is a fellow of American Statistical association.
His area of expertise includes statistical inference, Shrinkage estimation, HDA and asymptotic theory. He has numerous published
articles in scientific journals, both collaborative and methodological. Further, he has written several books, co-edited two volumes
and organized many invited sessions and workshops. He made several invited scholarly presentations in various countries.
Dr Ahmed serves on the editorial board of many statistical journals and book review editor for Technometrics. He served as a
Board of Director and Chairman of the Education Committee of the Statistical Society of Canada. He is VP communication for
ISBIS. Currently, he is serving as a member of an Evaluation Group, Discovery Grants and the Grant Selection Committee, Natural
Sciences and Engineering Research Council of Canada (NSERC).
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