Case influence diagnostics for the significance of the linear regression model

Abstract

In this paper we propose influence measures for two basic goodness-of-fit statistics, the coefficient of determination R 2 and test statistic F in the linear regression model using the deletion method. Some useful lemmas are provided. We also express the influence measures in terms of basic building blocks such as residual, leverage, and deviation that showed them as increasing function of residuals and a decreasing function of deviation. Further, the proposed measure reduces computational burden from O(n) to O(1). As illustrative examples, we applied the proposed measures to the stackloss data sets. We verified that deletion of one or few influential observations may result in big change in R 2 and F-statistic.

Effect of outliers on the variable selection by the regularized regression

“…In this paper, we focus the influence of one or few observations on the variable selection by the LASSO using the deletion method. The influence on the variable selection in the classical model via the least squares was studied by Bae et al (2017), and the selection of a smoothing parameter in the robust LASSO was done by Kim and Lee (2017).…”