A NOTE ON STRONG-CONVERGENCE RATES IN NONPARAMETRIC REGRESSION

The strong convergence rates in nonparametric regression estimation have been mostly discussed when the error variables in the regression models have finite variances. A few recent studies concern heavy-tailed error distributions for two comparable methods using the kernel and the k-nearest neighbor estimators. The obtained convergence rates are however noncomparable. Assuming the error variables have finite pth moments for the same p, 1 < p < 2, we derive comparable strong convergence rates far these two estimators via a unified approach. This improves the existing results for both the kernel estimator and the k-nearest neighbor estimator.