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

摘要

This paper proposes statistical procedures to check if a real-valued covariate X has an effect on a functional response Y(t). A non-parametric kernel regression is considered to estimate the influence of X on Y(t) and two test statistics based on residual sums of squares and smoothing residuals are proposed. Their acceptance levels are determined by means of permutations. The lack-of-fit test for a class of parametric models is then discussed as a consequence of the no effect procedure. Monte Carlo simulations provide an insight into the level and the power of the no effect tests. A study of atmospheric radiation illustrates the behavior of the proposed methods in practice.