The Penalized Analytic Center Estimator

Keith Knight

Econometric Reviews, 2016, vol. 35, issue 8-10, 1471-1484

Abstract: In a linear regression model, the Dantzig selector (Candès and Tao, 2007) minimizes the L 1 norm of the regression coefficients subject to a bound λ on the L ∞ norm of the covariances between the predictors and the residuals; the resulting estimator is the solution of a linear program, which may be nonunique or unstable. We propose a regularized alternative to the Dantzig selector. These estimators (which depend on λ and an additional tuning parameter r ) minimize objective functions that are the sum of the L 1 norm of the regression coefficients plus r times the logarithmic potential function of the Dantzig selector constraints, and can be viewed as penalized analytic centers of the latter constraints. The tuning parameter r controls the smoothness of the estimators as functions of λ and, when λ is sufficiently large, the estimators depend approximately on r and λ via r / λ -super-2.

Date: 2016
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DOI: 10.1080/07474938.2015.1092800

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