Adaptive Global Testing for Functional Linear Models

Jing Lei

Journal of the American Statistical Association, 2014, vol. 109, issue 506, 624-634

Abstract: This article studies global testing of the slope function in functional linear regression models. A major challenge in functional global testing is to choose the dimension of projection when approximating the functional regression model by a finite dimensional multivariate linear regression model. We develop a new method that simultaneously tests the slope vectors in a sequence of functional principal components regression models. The sequence of models being tested is determined by the sample size and is an integral part of the testing procedure. Our theoretical analysis shows that the proposed method is uniformly powerful over a class of smooth alternatives when the signal to noise ratio exceeds the detection boundary. The methods and results reflect the deep connection between the functional linear regression model and the Gaussian sequence model. We also present an extensive simulation study and a real data example to illustrate the finite sample performance of our method. Supplementary materials for this article are available online.

Date: 2014
References: Add references at CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2013.856794 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:109:y:2014:i:506:p:624-634

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2013.856794

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().