## Bernoulli

• Bernoulli
• Volume 19, Number 5A (2013), 2120-2151.

### 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.

#### Article information

Source
Bernoulli, Volume 19, Number 5A (2013), 2120-2151.

Dates
First available in Project Euclid: 5 November 2013

https://projecteuclid.org/euclid.bj/1383661216

Digital Object Identifier
doi:10.3150/12-BEJ446

Mathematical Reviews number (MathSciNet)
MR3129046

Zentralblatt MATH identifier
06254556

#### Citation

Horváth, Lajos; Reeder, Ron. A test of significance in functional quadratic regression. Bernoulli 19 (2013), no. 5A, 2120--2151. doi:10.3150/12-BEJ446. https://projecteuclid.org/euclid.bj/1383661216

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