Robust Regression Diagnostics With Data Transformations

Abstract

The problems of non-normality or functional relationships between variables may often be simplified by an appropriate transformation. However, the evidence for transformations may sometimes depend crucially on one or a few observations. Therefore, the purpose of the paper is to develop a method that will not be influenced by potential outliers during the process of data transformations. The concepts of the least trimmed squares estimator and the trimmed likelihood estimator are used to obtain the robust transformation parameters. Furthermore, the proposed procedure unifies robust statistics and a diagnostic approach to deal with the outlier problem in the regression transformation.