Consistent Variable Selection for High-dimensional Nonparametric Additive Nonlinear Systems

In this paper, the problem of variable selection is addressed for high-dimensional nonparametric additive nonlinear systems. The purpose of variable selection is to determine contributing additive functions and to remove non-contributing ones from the underlying nonlinear system. A two-step method is developed to conduct variable selection. The first step is concerned with estimating each additive function by virtue of kernel-based nonparametric approaches. The second step is to apply a nonnegative garrote estimator to identify which additive functions are nonzero in terms of the obtained non parametric estimates of each function. The proposed variable selection method is workable without suffering from the curse of dimensionality, and it is able to find the correct variables with probability one under weak conditions as the sample size approaches infinity. The good performance of the proposed variable selection method is demonstrated by a numerical example.