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Computational outlier detection methods in sliced inverse regression

Hadrien Lorenzo 1 Jérôme Saracco 2, 1 
1 ASTRAL - Méthodes avancées d’apprentissage statistique et de contrôle
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, Bordeaux INP - Institut Polytechnique de Bordeaux, Naval Group
Abstract : Sliced inverse regression (SIR) focuses on the relationship between a dependent variable y and a p-dimensional explanatory variable x in a semiparametric regression model in which the link relies on an index x β and link function f. SIR allows to estimate the direction of β that forms the effective dimension reduction (EDR) space. Based on the estimated index, the link function f can then be nonparametrically estimated using kernel estimator. This two-step approach is sensitive to the presence of outliers in the data. The aim of this paper is to propose computational methods to detect outliers in that kind of single-index regression model. Three outlier detection methods are proposed and their numerical behaviors are illustrated on a simulated sample. To discriminate outliers from "normal" observations, they use IB (in-bags) or OOB (out-of-bags) prediction errors from subsampling or resampling approaches. These methods, implemented in R, are compared with each other in a simulation study. An application on a real data is also provided.
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https://hal.inria.fr/hal-03369250
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Submitted on : Thursday, October 7, 2021 - 11:32:27 AM
Last modification on : Friday, February 4, 2022 - 3:23:47 AM
Long-term archiving on: : Saturday, January 8, 2022 - 6:39:05 PM

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Hadrien Lorenzo, Jérôme Saracco. Computational outlier detection methods in sliced inverse regression. Advances in Contemporary Statistics and Econometrics, Springer International Publishing, pp.101-122, 2021, ⟨10.1007/978-3-030-73249-3_6⟩. ⟨hal-03369250⟩

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