No effect and lack-of-fit permutation tests for functional regression (Q964615)

A nonparametric regression model with functional response \(Y(\cdot)\in L_2\) and a real-valued covariate \(X\) is considered. The no effect hypothesis is tested, i.e., \(H_0\): \(E(Y(t)| X=x)=\mu(x)\) does not depend on \(x\). A nonparametric modification of \(F\)-statistics and a smoothing residuals test statistic are used to construct a permutation test for \(H_0\). Analogous idea is proposed for testing lack-of-fit of some parametric hypothesis. Results of simulations and an application to vertical atmospheric radiation profiles data are presented.