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Published December 2007 | Published
Journal Article Open

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


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?

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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