Computational Outlier Detection Methods in Sliced Inverse Regression

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.