CONFIDENCE-REGIONS IN NONPARAMETRIC REGRESSION

Two methods for constructing confidence regions for the values of a re gression function at design points are presented. The approach is base d on finding vectors for which the (average) squared error loss associ ated with a kernel estimator is less than certain bounds. The bandwidt h for the kernel estimator can be chosen by any of the standard bandwi dth selectors. The proposed regions are shown to be valid for large sa mples in the sense that the asymptotic coverage probability is at leas t 1-alpha for any specified alpha is-an-element-of (0, 1).