SEARCH FOR SIGNIFICANT VARIABLES IN NONPARAMETRIC ADDITIVE REGRESSION

Nonparametric additive regression is studied under the assumption that only a subset of nonparametric components is nonzero. Each of these n onzero components depends on its own particular explanatory variable, called a significant variable. The search problem for significant vari ables is considered and an algorithm is proposed which guarantees expo nentially decreasing error probabilities as the sample size grows. We show that it is reasonable to use a rough bin estimator rather than to estimate the nonparametric components with the fastest possible rate.