A goodness-of-fit test for the functional linear model with scalar response

In this work, a goodness-of-fit test for the null hypothesis of a functional linear model with scalar response is proposed. The test is based on a generalization to the functional framework of a previous one, designed for the goodness-of-fit of regression models with multivariate covariates using random projections. The test statistic is easy to compute using geometrical and matrix arguments, and simple to calibrate in its distribution by a wild bootstrap on the residuals. The finite sample properties of the test are illustrated by a simulation study for several types of basis and under different alternatives. Finally, the test is applied to two datasets for checking the assumption of the functional linear model and a graphical tool is introduced. Supplementary materials are available online.Comment: Paper: 17 pages, 2 figures, 3 tables. Supplementary material: 8 pages, 6 figures, 10 table

Robust Functional Regression for Outlier Detection

In this paper we propose an outlier detection algorithm for temperature sensor data from jet engine tests. Effective identification of outliers would enable engine problems to be examined and resolved efficiently. Outlier detection in this data is challenging because a human controller determines the speed of the engine during each manoeuvre. This introduces variability which can mask abnormal behaviour in the engine response. We therefore suggest modelling the dependency between speed and temperature in the process of identifying abnormalities. The engine temperature has a delayed response with respect to the engine speed, which we will model using robust functional regression. We then apply functional depth with respect to the residuals to rank the samples and identify the outliers. The effectiveness of the outlier detection algorithm is shown in a simulation study. The algorithm is also applied to real engine data, and identifies samples that warrant further investigation