Statistica Sinica 14(2004), 1239-1257
AN 
TEST FOR LINEAR MODELS WITH
FUNCTIONAL RESPONSES
Qing Shen and Julian Faraway
Edmunds.com and University of Michigan
Abstract:
Linear models where the response is a function, but the predictors
are vectors are considered. A functional test for choosing among two nested
functional linear models is developed. Its null distribution is
derived and a convenient approximation is presented. A simple way
to test individual predictors is presented.
The test is applied to some data from Ergonomics and compared to
some competing tests. The ability to detect certain types of
differences between models is explored. A simulation study is
conducted to assess the size and power of the tests.
Key words and phrases:
ANOVA model, F test, functional data analysis, power, regression.