2021/04/22 by Toshiaki Tsukurimichi, I. Yu, Tsukurimichi, Toshiaki +6 · 2 citations
Computer Science · Decision Sciences · Engineering · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #Fault Detection and Control Systems #Machine Learning (cs.LG) #Machine Learning (stat.ML) #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2104.10840
openalex publication_date 2021/04/22 · arxiv created 2022/01/02 · arxiv updated 2022/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.