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Robust Function-on-Function Regression

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>31/07/2021
<mark>Journal</mark>Technometrics
Issue number3
Volume63
Number of pages11
Pages (from-to)396-409
Publication StatusPublished
Early online date14/09/20
<mark>Original language</mark>English

Abstract

Functional linear regression is a widely used approach to model functional responses with respect to functional inputs. However, classical functional linear regression models can be severely affected by outliers. We therefore introduce a Fisher-consistent robust functional linear regression model that is able to effectively fit data in the presence of outliers. The model is built using robust functional principal component and least squares regression estimators. The performance of the functional linear regression model depends on the number of principal components used. We therefore introduce a consistent robust model selection procedure to choose the number of principal components. Our robust functional linear regression model can be used alongside an outlier detection procedure to effectively identify abnormal functional responses. A simulation study shows our method is able to effectively capture the regression behaviour in the presence of outliers, and is able to find the outliers with high accuracy. We demonstrate the usefulness of our method on jet engine sensor data. We identify outliers that would not be found if the functional responses were modelled independently of the functional input, or using non-robust methods.