We consider partial sums of i.i.d. random variables with moments E(X1)=0, E(X12)=[sigma]2 and and show thatwith some explicit function [phi](·). A related result for random variables with exponentially thin tails has recently been shown by Steinebach, extending a result given by Shao.

We discuss almost sure versions of distributional limit theorems for central and intermediate order statistics.

We prove an almost sure version of a maximum limit theorem using logarithmic means and show that essentially only logarithmic means work as it is the case for almost sure central limit theorems.

We consider the problem of estimating a class of smooth functions defined everywhere on a real line utilizing nonparametric kernel regression estimators. Such functions have an interpretation as signals and are common in communication theory. Furthermore, they have finite energy, bounded...