Journal
BIOMETRIKA
Volume 97, Issue 2, Pages 465-480Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asq017
Keywords
Normal scale mixture; Ridge regression; Robustness; Shrinkage; Sparsity; Thresholding
Funding
- IBM at the University of Chicago Booth School of Business
- National Science Foundation, U.S.A
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This paper proposes a new approach to sparsity, called the horseshoe estimator, which arises from a prior based on multivariate-normal scale mixtures. We describe the estimator's advantages over existing approaches, including its robustness, adaptivity to different sparsity patterns and analytical tractability. We prove two theorems: one that characterizes the horseshoe estimator's tail robustness and the other that demonstrates a super-efficient rate of convergence to the correct estimate of the sampling density in sparse situations. Finally, using both real and simulated data, we show that the horseshoe estimator corresponds quite closely to the answers obtained by Bayesian model averaging under a point-mass mixture prior.
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