Let (X1, Y1), … , (Xn, Yn) be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima max( Xi) and max(Yi) is then characterized by the...

Let U1, U2,... be a sequence of independent r.v.'s having the uniform distribution on (0, 1). Let Fn be the empirical distribution based on the transformed uniform spacings Di,n:=G(nDi,n), i = 1, 2,..., n, where G is the exp(1) d.f. and Di,n is the ith spacing based on U1, U2,...,Un-1. The main...

Let Fn and Gn denote the Kaplan-Meier product-limit estimators of lifetime distributions based on two independent samples, and let Fninv and Gninv denote their quantile functions. We consider the corresponding P-P plot Fn(Gninv) and Q-Q plot Fninv(Gn), and establish strong approximations of...

Necessary and sufficient conditions for weak convergence and strong (functional) limit theorems for the negative parts of weighted multivariate empirical processes are obtained. These results are considerably different from those for the positive parts (or absolute values) of these processes....