The main objective for this paper is twofold. We first present a method for the derivation of an arbitrarily exact approximation to the distribution of Cramér-von Mises type functionals of any given Gaussian process X = {X(t): 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1}....

Motivated by problems in functional data analysis, in this paper we prove the weak convergence of normalized partial sums of dependent random functions exhibiting a Bernoulli shift structure.

Trimming is a standard method to decrease the effect of large sample elements in statistical procedures, used, e.g., for constructing robust estimators and tests. Trimming also provides a profound insight into the partial sum behavior of i.i.d. sequences. There is a wide and nearly complete...

A maximum-likelihood-type statistic is derived for testing a sequence of observations for no change in the parameter against a possible change. We prove that the limit distribution of the suitably normalized and centralized statistic is double exponential under the null hypothesis.

We find a necessary and sufficient condition for the weak convergence of the uniform empirical and quantile processes to a Brownian bridge in weighted Lp-distances. Under the same condition, weighted Lp-functionals of the uniform empirical and quantile processes converge in distribution to the...

In this paper we study ratios of local times of a random walk in random environment. Strong and weak limit theorems are obtained.

We develop a strong approximation of renewal processes. The consequences of this approximation are laws of the iterated logarithm and a Bahadur-Kiefer representation ofthe renewal process in terms of partial sums. The Bahadur-Kiefer representation implies that the rate of the strong...

We show that most random walks in the domain of attraction of a symmetric stable law have a non-trivial almost sure central limit theorem with the normal law as the limit.

We study the detection of a possible change in a stationary autoregressive process of order r. The test statistics are based on weighted supremum and Lp-functionals of the residual sums. Some limit theorems are proven under necessary and sufficient conditions.

We obtain a strong approximation for the logarithmic average of sample extremes. The central limit theorem and laws of the iterated logarithm are immediate consequences.