  This work investigates the problem of testing whether $d$ functional random
variables are jointly independent using a modified estimator of the
$d$-variable Hilbert Schmidt Indepedence Criterion ($d$HSIC) which generalizes
HSIC for the case where $d \geq 2$. We then get asymptotic normality of this
estimator both under joint independence hypothesis and under the alternative
hypothesis. A simulation study shows good performance of the proposed test on
finite sample.
