A Geometrical Method for Removing Edge Effects from Kernel-Type Nonparametric Regression Estimators

We introduce a simple geometric method for removing edge effects from kernel-type nonparametric regression estimators. It involves reflecting the data set in two estimated points, thereby generating a new data set with three times the range of the original data. The usual kernel-type estimator may be applied to the new, enlarged data set, without any danger of edge effects. This technique is applicable generally to both regularly spaced and randomly spaced designs and admits a natural analog of leave-one-out cross-validation. The new cross-validation algorithm may be extended to the very ends of the design interval, unlike its more conventional counterpart, which must be downweighted at the ends of the interval to avoid edge effects.