Computational Outlier Detection Methods in Sliced Inverse Regression

Hadrien Lorenzo () and Jérôme Saracco ()
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Hadrien Lorenzo: Inria BSO
Jérôme Saracco: Inria BSO & ENSC Bordeaux INP

A chapter in Advances in Contemporary Statistics and Econometrics, 2021, pp 101-122 from Springer

Abstract: 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 $$x'\beta $$ x ′ β and link function f. SIR allows estimating the direction of $$\beta $$ 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-73249-3_6

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DOI: 10.1007/978-3-030-73249-3_6

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