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Testing for lack of dependence in the functional linear model
Author(s) -
Kokoszka Piotr,
Maslova Inga,
Sojka Jan,
Zhu Lie
Publication year - 2008
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.5550360203
Subject(s) - principal component analysis , test statistic , mathematics , limiting , distribution (mathematics) , statistics , linear model , statistic , simple (philosophy) , econometrics , statistical hypothesis testing , mathematical analysis , engineering , mechanical engineering , philosophy , epistemology
The authors consider the linear model Y n = ψX n + ϵ n relating a functional response with explanatory variables. They propose a simple test of the nullity of ψ based on the principal component 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.