  Recently, the data-selective adaptive Volterra filters have been proposed;
however, up to now, there are not any theoretical analyses on its behavior
rather than numerical simulations. Therefore, in this paper, we analyze the
robustness (in the sense of l2-stability) of the data-selective Volterra
normalized least-mean-square (DS-VNLMS) algorithm. First, we study the local
robustness of this algorithm at any iteration, then we propose a global bound
for the error/discrepancy in the coefficient vector. Also, we demonstrate that
the DS-VNLMS algorithm improves the parameter estimation for the majority of
the iterations that an update is implemented. Moreover, we prove that if the
noise bound is known, we can set the DS-VNLMS so that it never degrades the
estimate. The simulation results corroborate the validity of the executed
analysis and demonstrate that the DS-VNLMS algorithm is robust against noise,
no matter how its parameters are adopted.
