Strong consistency of kernel-based local variable selection for nonlinear nonparametric systems

Local variable selection by first order expansion for nonlinear nonparametric systems is investigated in the paper. By substantially modifying the algorithms developed in our earlier work, the previous results have been considerably strengthened under much less restrictive conditions. Precisely, the estimates generated by the modified algorithms are shown to have both the set and parameter convergence with probability one, rather than only the set convergence in probability given in our earlier work.