TY - JOUR

T1 - Robust Function-on-Function Regression

AU - Hullait, Harjit

AU - Leslie, David

AU - Pavlidis, Nicos

AU - King, Steve

PY - 2021/7/31

Y1 - 2021/7/31

N2 - 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.

AB - 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.

KW - Outlier detection

KW - Robust functional data analysis

KW - Robust model selection

U2 - 10.1080/00401706.2020.1802350

DO - 10.1080/00401706.2020.1802350

M3 - Journal article

VL - 63

SP - 396

EP - 409

JO - Technometrics

JF - Technometrics

SN - 0040-1706

IS - 3

ER -