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Testing for lack of dependence in the functional linear model. (English) Zbl 1144.62316
Summary: The authors consider the linear model \(Y_n= \Psi X_n+ \varepsilon_n\) relating a functional response with explanatory variables. They propose a simple test of the nullity of \(\Psi\) based on principal components decomposition. The limiting distribution of their test statistic is chi-squared, but this distribution is also an excellent approximation in finite samples. The authors illustrate their method using data from terrestrial magnetic observatories.

62G10 Nonparametric hypothesis testing
62G08 Nonparametric regression and quantile regression
86A25 Geo-electricity and geomagnetism
62F03 Parametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
fda (R)
Full Text: DOI
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