The maximal correlation between a pair of [sigma]-fields and becomes arbitrarily small as sup{P(A [pitchfork] B) - P(A) P(B)/[P(A) P(B)]1/2, A [set membership, variant] , B [set membership, variant] , P(A) > 0, P(B) > 0} becomes sufficiently small.

A classification is given of all [sigma]-algebras that make two given [sigma]-algebras conditionally independent in the case that the [sigma]-algebras are generated by finite dimensional Gaussian random variables. In addition a classification is given of all Gaussian measures that have the...

For the problem of estimating the natural parameter of a p-dimensional exponential family, a characterization of regular limits of Bayes procedures is obtained which generalizes results of Sacks [14], Brown [3], and Berger and Srinivasan [1]. The form is deduced under regularity conditions for...

The general asymptotic order of magnitude is determined for the maximal deviation of the multivariate product-limit estimate from the estimated survival function on Rk. This order depends on the joint behavior of the censoring and censored distributions in a well-defined way. Corresponding to...

A new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions. It is shown that such processes may arise via natural generating procedures, and that, under very weak assumptions, that...

Strong laws of large numbers concerning nonnegative random variables are obtained and then they are utilized to establish stability results, among other things, for sums of pairwise independent random variables and the range of random walks.

The concept of the inverse correlation function of a stationary process was introduced by Cleveland (Technometrics 14 (1972), 277-293). The inverse partial correlation function of a stationary process may intuitively be thought of as the corresponding extension of the concept of the partial...

The aim of this paper is to examine the weak limiting behavior of upper and lower extremes from stationary sequences satisfying dependence conditions similar to D and D' introduced by Leadbetter (Z. Wahrsch. Verw. Gebiete 28 (1974), 289-303). By establishing the convergence in distribution of an...

This paper establishes several almost sure asymptotic properties of general autoregressive processes. By making use of these properties, we obtain a proof of the strong consistency of the least-squares estimates of the parameters of the process without any assumption on the roots of the...