Abstract
In this paper, we study the asymptotic properties of the adaptive Dantzig selector estimators in sparse high-dimensional linear regression models when the number of covariates $p$ may be large or even larger than the sample size $n$ at an exponential rate of the sample size $n$. When initial estimators, as the weights of the adaptive Dantzig selector, are consistent to constants, under regularity conditions, we show that the adaptive Dantzig selector has the Oracle property. Available initial estimators are also provided for both $p\leq n$ and $p>n$. Simulations are carried out to witness our theoretical conclusions.
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