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2016 ; 28
(4
): 813-838
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Classical Testing in Functional Linear Models
#MMPMID28955155
Kong D
; Staicu AM
; Maity A
J Nonparametr Stat
2016[]; 28
(4
): 813-838
PMID28955155
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We extend four tests common in classical regression - Wald, score, likelihood
ratio and F tests - to functional linear regression, for testing the null
hypothesis, that there is no association between a scalar response and a
functional covariate. Using functional principal component analysis, we
re-express the functional linear model as a standard linear model, where the
effect of the functional covariate can be approximated by a finite linear
combination of the functional principal component scores. In this setting, we
consider application of the four traditional tests. The proposed testing
procedures are investigated theoretically for densely observed functional
covariates when the number of principal components diverges. Using the
theoretical distribution of the tests under the alternative hypothesis, we
develop a procedure for sample size calculation in the context of functional
linear regression. The four tests are further compared numerically for both
densely and sparsely observed noisy functional data in simulation experiments and
using two real data applications.