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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.

MSC:
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
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fda (R)
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[1] Bosq, Linear Processes in Function Spaces (2000) · Zbl 0962.60004 · doi:10.1007/978-1-4612-1154-9
[2] Cai, Prediction in functional linear regression, The Annals of Statistics 34 pp 2159– (2006)
[3] Cardot, Testing hypothesis in the functional linear model, Scandinavian Journal of Statistics 30 pp 241– (2003)
[4] Cattell, The scree test for the number of factors, Journal of Multivariate Behavioral Research 1 pp 245– (1966)
[5] Chiou, Diagnostics for functional regression via residual processes, Computational Statistics and Data Analysis 15 pp 4849– (2007) · Zbl 1162.62394
[6] Chiou, Functional response models, Statistica Sinica 14 pp 675– (2004) · Zbl 1073.62098
[7] Cuevas, Linear functional regression: the case of fixed design and functional response, The Canadian Journal of Statistics 30 pp 285– (2002) · Zbl 1012.62039
[8] I. A. Daglis, J. U. Kozyra, Y. Kamide, D. Vassiliadis, A. S. Sharma, M. W. Liemohn, W. D. Gonzalez, B. T. Tsurutani & G. Lu (2003). Intense space storms: critical issues and open disputes. Journal of Geophysical Research, 108 (A5), 1208: http://www.agu.org/journals/ja/ia0305/2002JA009722/ doi:10.1029/2002JA009722, 2003.
[9] Ferraty, Nonparametric Functional Data Analysis: Theory and Practice (2006) · Zbl 1119.62046
[10] Gabrys, Portmanteau test of independence for functional observations, Journal of the American Statistical Association 102 (480) pp 1338– (2007) · Zbl 1332.62322
[11] Hall, On properties of functional principal components, Journal of Royal Statistical Society Series B 68 pp 109– (2006) · Zbl 1141.62048
[12] Hall, Theory for high-order bounds in functional principal components analysis (2007)
[13] Jach, Wavelet-based index of magnetic storm activity, Journal of Geophysical Research 111 pp A09215– (2006)
[14] Kamide, Current understanding of magnetic storms: Storm-substorm relationships, Journal of Geophysical Research 103 pp 17705– (1998)
[15] Kivelson, Introduction to Space Physics (1997)
[16] Kokoszka, Effect ofsubstroms on mid- and low-latitude horizontal intensity (2007)
[17] Müller, Generalized functional linear models, The Annals of Statistics 33 pp 774– (2005)
[18] Ramsay, Functional Data Analysis (2005) · Zbl 1079.62006 · doi:10.1002/0470013192.bsa239
[19] Rostoker, Effects of substorms on the stormtime ring current index Dst, Annales Geophysicae 18 pp 1390– (2000)
[20] Seber, Linear Regression Analysis (2003) · doi:10.1002/9780471722199
[21] W.-Y. Xu & Y. Kamide (2004). Decomposition of daily geomagnetic variations by using method of natural orthogonal component. Journal of Geophysical Research, 109 (A05218), doi:10.1029/2003JA010216, 2004; http://www.agu.org/pubs/crossref/2004/2003JA010216.shtml
[22] Yao, Functional linear regression analysis for longitudinal data, The Annals of Statistics 33 pp 2873– (2005)
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