Conditional selective inference for robust regression and outlier detection using piecewise-linear homotopy continuation

In this paper, we consider conditional selective inference (SI) for a linear model estimated after outliers are removed from the data. To apply SI framework, it is necessary to characterize events of how robust method identifies outliers. Unfortunately, existing SIs cannot be directly applied our problem because they applicable case where selection can represented by or quadratic constraints. We propose popular regressions such as least-absolute-deviation regression and Huber introducing new computational using convex optimization technique called homotopy method. show that proposed wide class outlier detection methods has good empirical performance on both synthetic data real experiments.