General linear hypothesis testing in functional response model

In this paper, the general linear hypothesis testing and variable selection problems in functional response model are considered. The globalizing pointwise F test and the $F_{\max }$-test as well as the variable selection methods based on multiple hypothesis testing are adapted to this model. The asymptotic null distributions and consistency under local alternatives of test statistics are established under some standard regularity conditions. Based on these results and nonparametric bootstrap approach, different methods are proposed to approximate the null distribution of test statistics. The performance of the new testing and variable selection procedures is compared with that of the known methods in numerical experiments based on real data set. The results suggest that the new methods often outperform the known ones in terms of size control, power and ability to detect significant variables.