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Abstract:
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The variable selection and estimation problem has received a great deal of attention in the statistics literature. Recently, methods for variable selection and estimation based on the normal score equations have been proposed [the Dantzig selector, (Candes and Tao, 2005)]. Finite sample properties of the Dantzig selector have been studied, however, large sample results for the Dantzig selector are lacking from the literature. We find large sample asymptotics for the Dantzig selector and establish that for certain patterns of predictor values the Dantzig selector is not consistent for model selection. We propose generalizations of the Dantzig selector which are consistent for model selection regardless of predictor values. The computational costs of our methods are comparable to those of the Dantzig selector. We study the performance of our methods via simulation.
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