Comparing the Proposed Sub-Ridge Regression with Ridge and OLS for A Shrinkage Factor; Data with or Without Multicollinearity

Abstract

1. The study considered the comparisons of the proposed sub-ridge regression method with ridge and OLS for shrinkage factor, for data with or without multi-collinearity. The various values of the shrinkage factor k were simulated and tested for ridge and sub-ridge regression and the results were compared with the Ordinary Least Square analysis initially done for three different sample sizes, 50, 75 and 100 for five economic data and they were, Exchange rate, Unemployment, Inflation. The value of k=0.0000005 was proposed as the convergent factor for which the Sub-Ridge becomes equal to the OLS parameters. As the k value decreases, the sum of square error of the Sub-Ridge regression parameters also decreases, for k=0.000007 the sum of square of the Sub-Ridge became equal to the sum of square error of the Ridge. The study recommended among other things that, even in the absence of multi-collinearity, Ridge regression and Sub-Ridge regression can still be used in obtaining equal parameter estimates and equal sum of square errors with the Ordinary Least Square, but for k value of 0.000007 for Ridge and k value of 0.0000005 for Sub- Ridge.

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