How well do ridge parameter estimators proposed so far perform in terms of normality, outlier detection, and MSE criteria?

Abstract

Ridge regression is a commonly used prediction method in cases of multicollinearity among regressors in multiple linear regression model. In this study, the performances of 366 different estimators proposed in the literature for ridge parameter estimation were evaluated. The criteria of estimators’ ratio of generating outliers and the proportion of normality besides the Mean Square Error (MSE) criterion were used for diagnosing ridge parameter estimators. Besides, the effect of outliers and deviations from normality generated by the ridge parameter estimators on the MSE was revealed by Spearman’s Rho correlation analysis. To do so, a Monte Carlo simulation was designed for 2420 different cases, considering the simulation parameters comprehensively in terms of the number of regressors, sample size, collinearity level and error variances. The results revealed that some ridge parameter estimators recommended according to MSE criterion, do not perform well in terms of outlier generation and normality criteria. Significant inter-linear correlations were also found among the ridge parameter estimators’ MSE performance criterion, ratios of outlier generation criterion and normality criterion. Thus, it is suggested that an effective ridge parameter estimator should perform well in terms of outlier generation and normality criteria, as well as having small MSE value.

Keywords:

• Multicollinearity
• Multiple linear regression
• Outlier
• Ridge parameter
• Ridge regression

Disclosure statement

No potential conflict of interest was reported by the authors.