Confidence regions in non-parametric regression
提出了两种在非参数回归中构建置信区域的方法，基于核估计的平方误差损失，保证大样本下渐近覆盖概率至少为1-a。
Two methods for constructing confidence regions for the values of a regression function at design points are presented. The approach is based on finding vectors for which the (average) squared error loss associated with a kernel estimator is less than certain bounds. The bandwidth for the kernel estimator can be chosen by any of the standard bandwidth selectors. The proposed regions are shown to be valid for large samples in the sense that the asymptotic coverage probability is at least 1 - a for any specified a E (0, 1). Non-parametric function estimation techniques occupy an important role in current statisti- cal theory and practice. The properties of non-parametric point estimators have been extensively studied and are now well-understood in many cases. Unfortunately the associ- ated, and arguably more important, problem of constructing confidence intervals, bands or regions to accompany the point estimators remains without a satisfactory solution. In this paper we explore the properties of some new methods for obtaining confidence regions in non-parametric regression.