TY - JOUR
T1 - Testing for No Effect in Functional Linear Regression Models, Some Computational Approaches
AU - Cardot, Hervé
AU - Goia, Aldo
AU - Sarda, Pascal
PY - 2004/2
Y1 - 2004/2
N2 - The functional linear regression model is a regression model where the link between the response (a scalar) and the predictor (a random function) is expressed as an inner product between a functional coefficient and the predictor. Our aim is to test at first for no effect of the model, i.e., the nullity of the functional coefficient. A fully automatic permutation test based on the cross covariance operator of the predictor and the response is proposed. The model can be, in an obvious way, extended to the case of several functional predictors. When testing for no effect of some covariate on the response the permutation test is no longer valid. An alternative pseudo-likelihood ratio test statistic is then introduced. The procedure can be applied in some way to test partial nullity of a functional coefficient. All procedures are illustrated and compared by means of simulation studies.
AB - The functional linear regression model is a regression model where the link between the response (a scalar) and the predictor (a random function) is expressed as an inner product between a functional coefficient and the predictor. Our aim is to test at first for no effect of the model, i.e., the nullity of the functional coefficient. A fully automatic permutation test based on the cross covariance operator of the predictor and the response is proposed. The model can be, in an obvious way, extended to the case of several functional predictors. When testing for no effect of some covariate on the response the permutation test is no longer valid. An alternative pseudo-likelihood ratio test statistic is then introduced. The procedure can be applied in some way to test partial nullity of a functional coefficient. All procedures are illustrated and compared by means of simulation studies.
KW - Functional linear regression model
KW - Functional principal components analysis
KW - Permutation test
KW - Pseudo-likelihood ratio test
KW - Randomization
UR - http://www.scopus.com/inward/record.url?scp=1642405059&partnerID=8YFLogxK
U2 - 10.1081/SAC-120028440
DO - 10.1081/SAC-120028440
M3 - Article
SN - 0361-0918
VL - 33
SP - 179
EP - 199
JO - Communications in Statistics Part B: Simulation and Computation
JF - Communications in Statistics Part B: Simulation and Computation
IS - 1
ER -