Abstract
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 behavior 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 modeled independently of the functional input, or using nonrobust methods.
Highlights
Functional Linear Regression (FLR) in the function-on-function case (Ramsay and Dalzell, 1991) is a widely used technique for modelling functional responses with respect to functional inputs
We can see that the outliers from the Robust FLR (RFLR) model do not necessarily appear as abnormal if we look at the temperature curves directly
There exist a number of functional regression models for functional inputs and responses, these methods are not robust to outliers
Summary
Functional Linear Regression (FLR) in the function-on-function case (Ramsay and Dalzell, 1991) is a widely used technique for modelling functional responses with respect to functional inputs. An automated approach to identifying pass-off test segments that require closer inspection will enable a larger proportion of the pass-off data to be processed, and can improve the early identification of engine issues To achieve this goal it is first necessary to develop accurate models of the expected behaviour of a healthy engine during different manoeuvres. This naturally affects the TGT curves and can mask unusual behaviour arising from an engine issue.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
