F. G Otze’s scientific contributions

. We prove Edgeworth expansions for degenerate von Mises statistics like the Beran, Watson, and Cram'er-von Mises goodness-of-fit statistics. Furthermore, we show that the bootstrap approximation works up to an error of order O(N Gamma1=2 ) and that Bootstrap based confidence regions attain a prescribed confidence level up to the order O(n Gamma1 ). 1. Introduction, main results, and some examples Let fOmega ; A; Pg be a probability space, and let X : fOmega ; Ag ! f; Fg be a random variable. The distribution function of X will be denoted by F. Furthermore, we shall denote by X 1 ; X 2 ; ... independent copies of X. In this paper we consider various approximations for the (degenerate) von Mises statistic VN , 1 N N X j=1 N X k=1 H(X j ; X k ); 1 Research supported by the SFB 343 at Bielefeld. 2 Research supported by the SFB 343 and Graduiertenkolleg at the University of Bielefeld. 1991 Mathematics Subject Classification. Primary 62E20; secondary 60F05. Key wo...