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Extraction of as much information as possible from huge data is a burning issue in the modern statistics due to more variables as compared to observations therefore penalization has been employed to resolve that kind of issues. Many achievements have already been made by such penalization techniques. Due to the large number of variables in many research areas declare it a high dimensional problem and with this the sample correlation becomes very large. In this paper, we studied the maximum likelihood estimation of variable selection under smoothly clipped absolute deviation (SCAD) and Ridge penalties with ultra-high dimension settings to solve this problem. We established the oracle property of the proposed model under some conditions by following the theoretical method of Kown and Kim (2012) [19]. These result can greatly broaden the application scope of high-dimension data. Numerical studies are discussed to assess the performance of the proposed method. The SCAD-Ridge given better results than the Lasso, Enet and SCAD.

SCAD-Ridge Penalized Likelihood Estimators for Ultra-high Dimensional Models