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The Dantzig selector: Statistical estimation when p is much larger than n

Candes, Emmanuel and Tao, Terence (2007) The Dantzig selector: Statistical estimation when p is much larger than n. Annals of Statistics, 35 (6). pp. 2313-2351. ISSN 0090-5364. doi:10.1214/009053606000001523. https://resolver.caltech.edu/CaltechAUTHORS:20100219-092002261

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Abstract

In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y=Xβ+z, where β∈Rp is a parameter vector of interest, X is a data matrix with possibly far fewer rows than columns, n≪p, and the zi’s are i.i.d. N(0, σ^2). Is it possible to estimate β reliably based on the noisy data y?


Item Type:Article
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http://dx.doi.org/10.1214/009053606000001523 DOIUNSPECIFIED
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aos/1201012958PublisherUNSPECIFIED
Additional Information:© 2007 Institute of Mathematical Statistics. Received August 2005; revised March 2006. Supported in part by NSF Grant DMS-01-40698 and by an Alfred P. Sloan Fellowship. Supported in part by a grant from the Packard Foundation. Emmanuel Candès thanks Rob Nowak for sending him an early preprint, Hannes Helgason for bibliographical research on this project, Justin Romberg for his help with numerical simulations and Anestis Antoniadis for comments on an early version of the manuscript. We also thank the referees for their helpful remarks.
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Funding AgencyGrant Number
NSFDMS-01-40698
Alfred P. Sloan FellowshipUNSPECIFIED
Packard FoundationUNSPECIFIED
Subject Keywords:statistical linear model; model selection; ideal estimation; oracle inequalities; sparse solutions to underdetermined systems; l(1)-minimization; linear programming; restricted orthonormality; geometry in high dimensions; random matrices
Issue or Number:6
Classification Code:AMS 2000 subject classifications. Primary 62C05, 62G05; secondary 94A08, 94A12.
DOI:10.1214/009053606000001523
Record Number:CaltechAUTHORS:20100219-092002261
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100219-092002261
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17530
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:19 Feb 2010 19:00
Last Modified:08 Nov 2021 23:36

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