@MISC{Horowitz10theadaptive, author = {Joel L. Horowitz and Jian Huang}, title = {The adaptive Lasso under a . . . }, year = {2010} }

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Abstract

We consider estimation of a linear model in which a few coefficients are “large” and may be objects of substantive interest, whereas others are “small” but not necessarily zero. The number of small coefficients may exceed the sample size. It is not known which coefficients are large and which are small. The large coefficients can be estimated with a smaller mean-square error if the small coefficients can be identified and the covariates associated with them dropped from the model. We show that the adaptive LASSO distinguishes correctly between large and small coefficients with probability approaching 1 as the sample size increases. The results of Monte Carlo experiments and an empirical example show that the adaptive LASSO reduces the mean-square errors of the estimates of the large coefficients even in quite small samples.