The horseshoe estimator for sparse signals
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 t...
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| Veröffentlicht in: | Biometrika 2010-06, Vol.97 (2), p.465-480 |
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| container_end_page | 480 |
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| container_title | Biometrika |
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| creator | Carvalho, Carlos M. Polson, Nicholas G. Scott, James G. |
| description | 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. |
| doi_str_mv | 10.1093/biomet/asq017 |
| format | Article |
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Polson, Nicholas G. ; Scott, James G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c421t-f15f7f193cf2bb91c98625526fddb38df9f806a7982d0830f9b7a4f6eff0ffc13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Applications</topic><topic>Bayes estimators</topic><topic>Bayesian analysis</topic><topic>Bayesian networks</topic><topic>Biology, psychology, social sciences</topic><topic>Density estimation</topic><topic>Estimating techniques</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>General topics</topic><topic>Horseshoes</topic><topic>Mathematics</topic><topic>Maximum likelihood estimation</topic><topic>Modeling</topic><topic>Nonparametric inference</topic><topic>Normal scale mixture</topic><topic>Parametric inference</topic><topic>Parametric models</topic><topic>Probability and statistics</topic><topic>Ridge regression</topic><topic>Robustness</topic><topic>Sampling</topic><topic>Sciences and techniques of general use</topic><topic>Shrinkage</topic><topic>Signal noise</topic><topic>Simulation</topic><topic>Sparsity</topic><topic>Statistics</topic><topic>Studies</topic><topic>Threshing</topic><topic>Thresholding</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Carvalho, Carlos M.</creatorcontrib><creatorcontrib>Polson, Nicholas G.</creatorcontrib><creatorcontrib>Scott, James G.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>Biotechnology Research Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><jtitle>Biometrika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Carvalho, Carlos M.</au><au>Polson, Nicholas G.</au><au>Scott, James G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The horseshoe estimator for sparse signals</atitle><jtitle>Biometrika</jtitle><date>2010-06-01</date><risdate>2010</risdate><volume>97</volume><issue>2</issue><spage>465</spage><epage>480</epage><pages>465-480</pages><issn>0006-3444</issn><eissn>1464-3510</eissn><coden>BIOKAX</coden><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.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><doi>10.1093/biomet/asq017</doi><tpages>16</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0006-3444 |
| ispartof | Biometrika, 2010-06, Vol.97 (2), p.465-480 |
| issn | 0006-3444 1464-3510 |
| language | eng |
| recordid | cdi_proquest_journals_347005426 |
| source | RePEc; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Oxford University Press Journals All Titles (1996-Current); Alma/SFX Local Collection |
| subjects | Applications Bayes estimators Bayesian analysis Bayesian networks Biology, psychology, social sciences Density estimation Estimating techniques Estimators Exact sciences and technology General topics Horseshoes Mathematics Maximum likelihood estimation Modeling Nonparametric inference Normal scale mixture Parametric inference Parametric models Probability and statistics Ridge regression Robustness Sampling Sciences and techniques of general use Shrinkage Signal noise Simulation Sparsity Statistics Studies Threshing Thresholding |
| title | The horseshoe estimator for sparse signals |
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