# zbMATH — the first resource for mathematics

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
##### Keywords:
geomagnetism; independence test
fda (R)
Full Text:
##### References:
 [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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.