Bootstrap estimation of the proportion of outliers in robust regression

This paper presents a nonparametric bootstrap method for estimating the proportions of inliers and outliers in robust regression models. Our approach is based on the concept of stability, providing robustness against distributional assumptions and eliminating the need for pre-specified confidence levels. Through numerical experiments, we demonstrate that this method yields more accurate and stable estimates than existing alternatives. Additionally, the generated instability paths offer a valuable graphical tool for understanding the inlier and outlier distributions within the data. The method naturally extends to generalized linear models, where we find that variance-stabilizing transformations produce residuals that are well-suited for outlier detection. Applications to two real-world datasets further illustrate the practical utility of our approach in identifying outliers.