Aldous and Hoover have proved independently that an array X = (Xij, i, j [set membership, variant] ) of random variables is exchangeable under separate or joint permutations of rows and columns, iff a.s. Xij[reverse not equivalent]f([alpha], [xi]i, [eta]j, [xi]ij) or Xij[reverse not...

Several [alpha]-stable limit theorems for sums of dependent random vectors are proved via point processes theory; p-mixing, m-dependence, and the type of mixing treated within the extreme value theory are considered.

It is shown that the level-crossings process of zeroes and ones corresponding to a stationary but not independent Gaussian sequence can never be exactly (m-step) Markov, although its correlation-sequence can agree exactly with that of a Markov sequence.

The nonparametric estimation results for time series described in the literature to date stem fairly directly from a seminal work of M. Rosenblatt. The gist of the current picture is that under either strong or G2 mixing, many properties of nonparametric estimation in the i.i.d. case carry over...

The consistency proof for the (Gaussian quasi) maximum likelihood estimator in multivariable ARMA models as given in Dunsmuir and Hannan (1976, Adv, in Appl. Probab. 8, 339-364) rests on a certain property of the underlying parameter space, called B6 in their paper. It is not known whether the...

Algorithms for determining the generating function, the prediction error matrix, and the best linear predictor for non-full-rank bivariate stationary stochastic processes are obtained.

Suppose (i1,n, ..., in,n) is permutation of (1, ..., n) for each positive integer n such that the order of the indices {1, h., n - 1} in the permutation corresponding to n - 1 is preserved. If {Zn} is a sequence of mean-zero random variables and {kn} is a sequence of positive integers with kn --...

Given a sequence of i.i.d. multinomial random vectors, each of the coordinates of the sum of the random vectors, multiplied by their respective indices in the sequence, is centered and normed by its conditional mean and conditional standard deviation, conditioned on the sum of the random...

The concept of weak convergence of measures on topological spaces depends on a topology of the space. In this paper we discuss the relationship between weak convergence of measures on a separable Hilbert space H equipped with w-* and strong topology. Starting from this point we rederive a...

In the balanced multivariate components of variance the likelihood ratio criterion depends on the roots of a determinantal equation involving the "between" and "within" matric sums of squares. The limiting distribution of -2 times the logarithm of the criterion is characterized; it is not a...