The horseshoe estimator for sparse signals
2010/04/28 by C. M. Carvalho, Carla M. Carvalho, N. G. Polson +3 · 1,442 citations
Mathematics · #Advanced Statistical Methods and Models #Algorithm #Applied mathematics #Computer science #Estimator #Horseshoe (symbol) #Mathematical optimization #Mathematics #Robustness (evolution) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics
paper · doi:10.1093/biomet/asq017
published in Biometrika 97(2), 465-480 (Oxford University Press)
openalex publication_date 2010/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Abstract
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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