 Testing Hypotheses in the Functional Linear ModelHervé Cardot, Frédéric Ferraty, André Mas and Pascal Sarda Scandinavian Journal of Statistics, 2003, vol. 30, issue 1, 241-255 Abstract: The functional linear model with scalar response is a regression model where the predictor is a random function defined on some compact set of ℝ and the response is scalar. The response is modelled as Y=Ψ(X)+ɛ, where Ψ is some linear continuous operator defined on the space of square integrable functions and valued in ℝ. The random input X is independent from the noise ɛ. In this paper, we are interested in testing the null hypothesis of no effect, that is, the nullity of Ψ restricted to the Hilbert space generated by the random variable X. We introduce two test statistics based on the norm of the empirical cross‐covariance operator of (X,Y). The first test statistic relies on a χ2 approximation and we show the asymptotic normality of the second one under appropriate conditions on the covariance operator of X. The test procedures can be applied to check a given relationship between X and Y. The method is illustrated through a simulation study. Date: 2003 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:30:y:2003:i:1:p:241-255 Ordering information: This journal article can be ordered from Access Statistics for this article Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association |
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