Consistency of the kernel density estimator: a survey

Various consistency proofs for the kernel density estimator have been developed over the last few decades. Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand. While considering global properties of the empirical distribution functions is sufficient for strong consistency, proofs of exact convergence rates use deeper information about the underlying empirical processes. A unifying character, however, is that earlier and more recent proofs use bounds on the probability that a sum of random variables deviates from its mean.     

Individuelle Freiheit als Grundlage normativer Ökonomik

The economic approach to CSR has been increasingly criticized as being too narrow to provide a basis for ethical judgments. However, economic theory makes an implicit but fundamental ethical judgment as it emphasizes individual freedom, premising that everyone should be free to make their decisions in the marketplace. I interpret this ethical judgment explicitly and derive three implications, which allow assessing the legitimacy of corporate action in a globalized world. More specifically, I argue that contracts must rely on the voluntary and informed consent of all people concerned to be legitimate. Companies have the responsibility to ensure that these criteria are met in their contracts.     

Modellierung von Aktienanlagen bei laufenden Umschichtungen und einer Besteuerung von Veräußerungsgewinnen

This paper develops a technique which simplifies the calculation of terminal values of share investments when portfolio turnovers repeatedly trigger capital gains taxation. So far, the calculations of these values are difficult, due to recursive dependencies, which cannot be expressed by geometric series. Using our technique, tax burdens of differently taxed forms of share investments can be determined in an easy way even if these methods imply different elements of deferred taxation (equity funds, certificates, preferred taxed pension plans). The simplification is reached by assuming a specific trading strategy. This strategy is in line with empirically observed investor behavior which is characterized by periodical portfolio turnovers and reluctance to realize taxable capital gains.     

Editorial special issue: Statistics in sports

AStA Advances in Statistical Analysis - Triggered by advances in data gathering technologies, the use of statistical analyzes, predictions and modeling techniques in sports has gained a rapidly...