Abstract Let Y = m ( X )+ ϵ be a regression model with a dichotomous output Y and a step function m with exact one jump at a point θ and two different levels a and b . In the applied sciences the parameter θ is interpreted as a split-point whereas b and 1- a are known as positive and negative...

Abstract We consider the two-sample problem with dispersion alternatives. Starting with a sufficient characterization of the alternative by means of two integrals we come up with a test which is based on the empirical counterparts of the integrals. Especially the critical region is now the...

We give the optimal constants in the Marcinkiewicz–Zygmund inequalities for symmetric summands. As an application we substantially improve the estimates of Ren and Liang (2001) in the Marcinkiewicz–Zygmund–Hölder inequality and identify the best possible constants in the symmetric case.

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...

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...

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...

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...