A test of significance in functional quadratic regression

Abstract

We consider a quadratic functional regression model in which a scalar response depends on a functional predictor; the common functional linear model is a special case. We wish to test the significance of the nonlinear term in the model. We develop a testing method which is based on projecting the observations onto a suitably chosen finite dimensional space using functional principal component analysis. The asymptotic behavior of our testing procedure is established. A simulation study shows that the testing procedure has good size and power with finite sample sizes. We then apply our test to a data set provided by Tecator, which consists of near-infrared absorbance spectra and fat content of meat.

Published in at http://dx.doi.org/10.3150/12-BEJ446 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• Prediction in functional linear regression
• Methodology and convergence rates for functional linear regression
• Statistical inferences for functional data

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• On regularized polynomial functional regression
• Projection-based nonparametric goodness-of-fit testing with functional covariates