Testing for lack of dependence between functional variables

We introduce a test for the lack of dependence between two random variables valued into real Hilbert spaces. Here, we consider lack of dependence in the broader sense, that is, non-correlation. The test statistic is similar to the one proposed by Kokoszka et al. (2008) for testing for no effect in the linear functional model. The asymptotic distribution under the null hypothesis of this statistic is obtained as well as a consistency result for the proposed test. Applications to the case of functional variables are indicated and simulations show, in this context, the performance of the proposed method.