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In this paper, we study large sample properties of smoothly clipped absolute deviation (SCAD) penalized maximum likelihood estimation for highdimensional parameters. First, we prove that the oracle maximum likelihood estimator (MLE) asymptotically becomes a local maximizer of the SCAD-penalized log-likelihood, even when the number of parameters is much larger than the sample size; the oracle MLE is an ideal non-penalized MLE obtained by deleting all irrelevant parameters in advance. Second, wedoi:10.5705/ss.2010.027 fatcat:s7eg5sphp5ex3eprthovzkon2e