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Abstract: We propose an empirical Bayes method for variable selection and
coefficient estimation in linear regression models. The method is based on
a particular hierarchical Bayes formulation, and the estimator is shown to
be closely related to the LASSO estimator. Such a connection allows us to
take advantage of the recently developed quick LASSO algorithm to compute
the empirical Bayes estimate, and provides new ways to select the tuning
parameter in the LASSO method. Unlike previous empirical Bayes variable
selection methods, which in most practical situation can only be
implemented through a greedy stepwise algorithm, our method gives a global
solution efficiently. Simulations show that the proposed method compares
favorably with other variable selection and estimation methods in terms of
variable selection, estimation accuracy, and computation speed. This is
joint work with Professor Yi Lin.
