Open Access
VOL. 9 | 2013 Some asymptotic theory for functional regression with stationary regressor
Frits Ruymgaart, Jing Wang, Shih-Hsuan Wei

Editor(s) M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, M. H. Maathuis

Inst. Math. Stat. (IMS) Collect., 2013: 291-302 (2013) DOI: 10.1214/12-IMSCOLL921


The general asymptotic distribution theory for the functional regression model in Ruymgaart et al. [Some asymptotic theory for functional regression and classification (2009) Texas Tech University] simplifies considerably if an extra assumption on the random regressor is made. In the special case where the regressor is a stochastic process on the unit interval, Johannes [Privileged communication (2008)] assumes the regressor to be stationary, in which case the eigenfunctions of their covariance operator turn out to be known, so that only the eigenvalues are to be estimated. In the present paper we will also assume the eigenvectors to be known, but within an abstract setting. The simplification mentioned above is due to the circumstance that the covariance operator of the regressor commutes with its estimator as it can be constructed under the current conditions. Moreover, it is now possible to test linear hypotheses for the regression parameter that correspond to linear subspaces spanned by a finite number of the known eigenvectors.


Published: 1 January 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1347.60016
MathSciNet: MR3202641

Digital Object Identifier: 10.1214/12-IMSCOLL921

Primary: 60K35 , 60K35
Secondary: 60K35

Keywords: asymptotic distribution , functional regression , stationary regressor , testing linear hypotheses

Rights: Copyright © 2010, Institute of Mathematical Statistics

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