Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation

• URL: http://arxiv.org/abs/2104.10840v1
• Date: Thu, 22 Apr 2021 03:01:18 GMT
• Title: Conditional Selective Inference for Robust Regression and Outlier Detection using Piecewise-Linear Homotopy Continuation
• Authors: Toshiaki Tsukurimichi, Yu Inatsu, Vo Nguyen Le Duy, Ichiro Takeuchi
• Abstract summary: We consider statistical inference of model estimated after outliers are removed. We show that the proposed conditional SI method is applicable to a wide class of robust regression and outlier detection methods.
• Score: 16.443165965475096
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In practical data analysis under noisy environment, it is common to first use robust methods to identify outliers, and then to conduct further analysis after removing the outliers. In this paper, we consider statistical inference of the model estimated after outliers are removed, which can be interpreted as a selective inference (SI) problem. To use conditional SI framework, it is necessary to characterize the events of how the robust method identifies outliers. Unfortunately, the existing methods cannot be directly used here because they are applicable to the case where the selection events can be represented by linear/quadratic constraints. In this paper, we propose a conditional SI method for popular robust regressions by using homotopy method. We show that the proposed conditional SI method is applicable to a wide class of robust regression and outlier detection methods and has good empirical performance on both synthetic data and real data experiments.

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