New Approach to Variable Selection for Nonparametric Nonlinear Systems

Let the observation {u(k), y(k)} be generated by y(k+1) = f(y(k), ... , y(k+1-p), u(k), ... , u(k+1-q)) + epsilon(k+1)where (p, q) are the system orders, epsilon(k) is the system noise, and f(.) is an unknown nonlinear function. A new method for variable selection of f(.) at any interested points is introduced. In contrast to most of the existing results, the new method is not based on optimizing a certain criterion, and estimates from the variable selection algorithm given in this paper are easy to update computationally in comparison with the criterion-optimization-based methods when new data arrive. Under reasonable conditions the estimates are proved to converge to the true contributing variables with probability one.