Robust hypothesis testing in functional linear models

AbstractWe extend three robust tests – Wald-type, the likelihood ratio-type and F-type in functional linear models with scalar dependent variable covariate. Based on percentage of variance explained criterion, we use principal components analysis re-express a model to finite regression. We investigate theoretical properties these testing procedures assess sample through numerical simulation. In our experiments, power performance Type I error rates are studied separately sparsely densely models. The simulation results show that test more stable less sensitive heavy-tailed distributed errors than classical ones. Two real datasets analysed compare procedures.Keywords: Functional regressionfunctional componentsM-estimationrobust hypothesis AcknowledgmentsThe DTI data were collected at Johns Hopkins University Kennedy-Krieger Institute. also thank both StatLib original contributor dataset, for usage FCS data. authors would like two anonymous referees their helpful comments suggestions, which have led improvement this paper.Disclosure statementNo potential conflict interest was reported by authors.Additional informationFundingThis work is supported Natural Sciences Engineering Research Council Canada [RGPIN-2017-05720].