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, 1Strong convergence rates Kernel regression Nearest neighbor regression Random and constant regressors