A robust principal component analysis for samples from a bivariate distribution function is described. The method is based on robust estimators for dispersion in the univariate case along with a certain linearization of the bivariate structure. Besides the continuity of the functional defining...

The multitype branching diffusion (MBD) is considered. A review of the general theory of multitype point processes is given in Section 2, and spatial central limit theorems for homogeneous infinitely divisible processes are proven in Section 3. In Section 4, the MBD is defined, and equations for...

This work characterizes some subclasses of [alpha]-stable (0 [alpha] 1) Banach spaces in terms of the extendibility to Radon laws of certain [alpha]-stable cylinder measures. These result extend the work of S. Chobanian and V. Tarieladze (J. Multivar. Anal.7, 183-203 (1977)). For these spaces...

Let ([Omega],,P;z) be a probability space with an increasing family of sub-[sigma]-fields {z, z [set membership, variant] D}, where D = [0, [infinity]) - [0, [infinity]), satisfying the usual conditions. In this paper, the stochastic integral with respect to an z-adapted 2-parameter Brownian...

Let n denote the sample size, and let ri [set membership, variant] {1,...,n} fulfill the conditions ri - ri-1 = 5 for i = 1,...,k. It is proved that the joint normalized distribution of the order statistics Zri:n, i = 1,...,k, is independent of the underlying probability measure up to a...

The problem considered is that of estimating the integer or integers that prescribe the dimension of a linear system. These could be the Kronecker indices. Though attention is concentrated on the order or McMillan degree, which specifies the dimension of a minimal state vector, the same results...

In an earlier paper, the present author ([6], Calcutta Statist. Assoc. Bull.28, 47-56) proposed a similar test for a mean testing problem with additional observations on a set of correlated auxiliary variables. This idea has been extended here to cover some multivariate linear regression testing...

Let X([omega]) be a random element taking values in a linear space 4 endowed with the partial order <=; let 10 be the class of nonnegative order-preserving functions on 4 such that, for each g[set membership, variant]10, E[g(X)] is defined; and let 11n10 be the subclass of concave functions. A version of Markov's inequality for such spaces in P(X >= x) <= inf10E[g(X)]/g(x). Moreover, if E(X) = [xi] is defined and if Jensen's inequality applies, we have a further inequality P(X>=x) <= inf11E[g(X)]/g(x) <= inf11g([xi])/g(x). Applications are given using a variety or orderings of interest in statistics and applied probability.

Let {Xn, n = 1} be a real-valued stationary Gaussian sequence with mean zero and variance one. Let Mn = max{Xt, i <= n} and Hn(t) = (M[nt] - bn)an-1 be the maximum resp. the properly normalised maximum process, where cn = (2 log n)1/2, an = (log log n)/cn and . We characterize the almost sure limit functions of (Hn)n>=3 in the set of non-negative, non-decreasing, right-continuous, real-valued functions on (0, [infinity]), if r(n) (log n)3-[Delta] = O(1) for all [Delta] 0 or if r(n) (log...</=>

The paper deals with limit theorems for probabilities of large deviations for sums of independent identically distributed random vectors. We give more detailed bounds for the remainder in von Bahr's limit theorem. New asymptotic formulas for probabilities of large deviations on the outside of...