High-Dimensional Data Analysis: Comparison of LASSO, OLS Post LASSO With SCAD, MCP under Different Criteria
Author: Sara

The penalized least square estimator with Least Absolute Shrinkage and Selection Operator (LASSO), Minimax Concave Penalty (MCP) and Smoothly Clipped Absolute Deviation (SCAD) have attractive and efficient variable selection properties. The property of an oracle estimate and consistent selection of important variables are fulfilled by Smoothly Clipped Absolute Deviation and Minimax Concave Penalty method, whereas Least Absolute shrinkage and Selection Operator does not possess oracle property but consistently select the important variable. However, the efficiency of this penalization dependents on the appropriate selection of tuning parameter. Cross Validation, Generalized Cross Validation, AIC, and BIC are the most commonly used techniques for the selection of the tuning parameter. However, these techniques do not select the tuning parameter adequately and the resulting model lead with overfitting phenomena. Whereas AIC and BIC are inadequate for consistently selecting a true model. We use a universal penalty level to select appropriate tuning parameter under different noise levels and a varying number of variables to identify the true variables in the model. We examine the performance of the proposed procedure by numerical simulation and Boston House Price data Supervisor:- Dr Zahid Asghar

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Keywords : Cross Validation (CV), Least Absolute Shrinkage and Selection Operator (LASSO), Minimax Concave Penalty (MCP), Root Mean Square Error (RMSE), Smooth Clipped Absolute Deviation (SCAD), Tuning Parameter
Supervisor: Zahid Asghar

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