Influential diagnostics with Pena’s statistic for the modified ridge regression

Abstract

In a linear regression model, the estimation of regression parameters is affected by some anomalous observations in the data set. Thus, identification of these observations is one of the essential steps in regression analysis. Detection of these influential observations becomes more complex when serious multicollinearity among regressors is also observed. In the present article, we formulated Pena’s statistic for each point while considering the modified ridge regression (MRR) estimator. Using this statistic, we showed that when MRR was used to mitigate the effects of multicollinearity, the influence of some observations could be significantly changed. The normality of this statistic was also discussed and it was proved that it could detect a subset of high modified ridge leverage outliers. The Monte Carlo simulations were used for empirical results and an example of real data was presented for illustration.

Keywords:

• Case deletion
• Cook’s distance
• Ridge regression
• Modified ridge regression
• Multicollinearity
• Pena’s statistic

MATHEMATICAL SUBJECT CLASSIFICATION:

• 62J07
• 62J05
• 62F03