Abstract This article deals with estimation of the change-point in a sequence of independent random variables. It is based on a least squares process endowed with a weight function. For finite sample sizes we derive bounds of the error probability. They immediately yield rates of consistency...

Abstract. The crossing point of two different distribution functions may be of interest for different reasons. The comparison of two different production processes with respect to failures may be one field of application, since the point of intersection of the corresponding distribution...

In this article a systematic study is given of the asymptotic behavior of two-sample tests based on U-Statistics with arbitrary antisymmetric kernels ψ. Besides the investigation under the hypothesis and under fixed alternatives we determine the local power as a function of ψ as well as its...

Consider a triangular array of rowwise independent random elements with values in a measurable space. Suppose there exist [theta]n [set membership, variant]Tn={in-1: 1 [less-than-or-equals, slant]i[less-than-or-equals, slant]n-1} such that X1n,...,Xn,n[theta]n have distribution Pn and...

Let Y be a nonconstant Markov-Gaussian process with almost sure continuous sample functions. We show that with probability one the original process Y and the reflected process Y in each case attain their maximal value at precisely one point. Almost sure uniqueness of maximizers of stochastic...

In this paper we consider the classical problem of testing whether two samples of observations are from the same distribution. Since in many situations the data are multivariate or even of functional type, classical methodology is not applicable. In our approach we conceive a difference in...

We describe the limit distribution of V- and U-statistics in a new fashion. In the case of V-statistics the limit variable is a multiple stochastic integral with respect to an abstract Brownian bridge GQ. This extends the pioneer work of Filippova (1961) [8]. In the case of U-statistics we...

We consider a marked empirical process corresponding to a sample X1,...,Xn of independent and identically distributed random variables and exchangeable random marks C1,...,Cn. If the sum of all marks is equal to zero, then there exists a certain order statistic with random index, which is a...