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....

In the random censorship from the right model, strong and weak limit theorems for Bahadur-Kiefer type processes based on the product-limit estimator are established. The main theorm is sharp and may be considered as a final result as far as this type of research is concerned. As a consequence of...

Strong limit theorems are obtained for maximal and minimal multivariate kn-spacings, where {kn}n=1[infinity] is a sequence of positive integers satisfying kn = 0(log n). The shapes, in terms of which these spacings are defined, are allowed to be quite general. They must only satisfy certain...

We consider the local empirical process indexed by sets, a substantial generalization of the well-studied uniform tail empirical process. We show that the weak limit of weighted versions of this process is Poisson under certain conditions, whereas it is Gaussian in other situations. Our main...

A law of the iterated logarithm in "the middle" is established for weighted empirical processes based on a sequence of i.i.d. random vectors, uniformly distributed on the (multivariate) unit square. This result unifies several results in the literature.