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

Toshiaki Tsukurimichi (), Yu Inatsu (), Vo Nguyen Le Duy () and Ichiro Takeuchi ()
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Toshiaki Tsukurimichi: Nagoya Institute of Technology
Yu Inatsu: Nagoya Institute of Technology
Vo Nguyen Le Duy: Nagoya Institute of Technology
Ichiro Takeuchi: Nagoya Institute of Technology

Annals of the Institute of Statistical Mathematics, 2022, vol. 74, issue 6, No 7, 1197-1228

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

Keywords: Selective inference; Robust regression; Parametric programing; Outlier detection (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10463-022-00846-2

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