Let H be a Hilbert space and B(H) be the algebra of all bounded linear operators on H. Normal Hilbert B(H)-module valued processes are studied over a locally compact abelian group as models for infinite variate or Hilbert space valued stochastic processes. Harmonizability of Rozanov type and...

The work started by [4], Theory Probab. Appl. 15, 604-618], and continued by [6], Trans. Amer. Math. Soc. 263, 505-520], is extended, and completed with respect to certain aspects. Infinite-dimensional stochastic chains are considered in the framework of Mukherjea [loc. cit.]; backward products...

Let N points be arbitrarily chosen on the circle with unit circumference, and order them clockwise. The uniform mth order spacings are then defined as the clockwise distances between any pair of points having m - 1 other points in between. A Glivenko-Cantelli theorem and nonlinear almost sure...

In the linear model Y = X[beta] + u the question arises when a linear transformation z = Ly contains all information of the linear model. This problem was solved by[2], Drygas (, forthcoming) and [11]). As an application the estimation of the variance of the observations, its skewness, and its...

Let X1, X2,..., be a sequence of independent identically distributed random vectors in k-dimensional Euclidean space Rk and let [Phi](A) be the standard normal distribution in Rk, Sn = X1 + ... + Xn. In this paper a behavior of a relation P{1/[radical sign]nSn [set membership, variant]...

{W(x, y), x>=0, y>=0} be a Wiener process and let [eta](u, (x, y)) be its local time. The continuity of [eta] in (x, y) is investigated, i.e., an upper estimate of the process [eta]([mu], [x, x + [alpha]) - [y, y + [beta])) is given when [alpha][beta] is small.

Tests of total independence of d (>=2) random variables are proposed using the empirical characteristic function. The approach is parallel to that of Hoeffding, Blum, Kiefer, and Rosenblatt.

It is shown that the likelihood ratio of an autoregressive time series of finite order with a regression trend is asymptotically normal. This result is used to derive the power of a test for positive correlation of the residuals under local autoregressive alternatives. The test is based on the...

A result by [9], 1-21) on the essential completeness of the class of nonrandomized deicision rules is generalized to a statistical decision model with noncompact decision space. The generalized result is obtained as a direct consequence of an existence result for an allocation problem arising in...

Three limit theorems describing asymptotic distribution of vacancy in general multivariate coverage problems are proved, in which n k-dimensional spheres are distributed within a k-dimensional unit cube according to a density f. The first result (a central limit theorem) describes the case where...