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

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. A lot of achievements have already been made by such 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 order to solve this problem, in this paper we discuss the maximum likelihood estimation of variable selection under smoothly clipped deviation (SCAD) and Ridge penalties with ultra-high dimension settings. Following the theoretical method of Kown and Kim (2012)[19] and under some conditions we established the oracle property of the proposed model. These results can easily be extended to the application scope of high-dimension data. Numerical studies are discussed to assess the performance of the proposed method. The SCAD-Ridge gives better results than the Lasso, Enet and SCAD.