Showing papers in "Journal of Multivariate Analysis in 1983"

TL;DR: In this article, it was shown that the central limit theorem holds for some non-linear functionals of stationary Gaussian fields if the correlation function of the underlying field tends fast enough to zero.

TL;DR: In this paper, the authors established several almost sure asymptotic properties of general autoregressive processes and obtained 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 characteristic polynomial.

TL;DR: In this paper, a new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions, and it is shown that such processes may arise via natural generating procedures, and that they can be approximated as closely as desired by appropriate finite models.

TL;DR: In this article, it was shown that under general conditions, and in particular assuming only a finite 2nd moment, maxωI(ω{2πf(ω)logT} ≤ 1, a.s., and under stricter conditions it is shown that equality holds.

TL;DR: A random vector is said to have a 1-symmetric distribution if its characteristic function is of the form φ(|t1| + … + |tn|) as discussed by the authors.

TL;DR: In this paper, 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.

TL;DR: The existence of limit spectral distribution of the product of two independent random matrices is proved when the number of variables tends to infinity as discussed by the authors, where the Wishart matrix is a symmetric nonnegative definite matrix.

TL;DR: In this article, a generalized type of near neighbor estimator is proposed, where the window size is chosen as a function of near neighbour distances, rather than actually equal to one of the distances.

TL;DR: In this paper, the class of all limit measures of a strongly continuous one-parameter group of operators on a Banach space X and a subset of a set J (X) of all probability measures on X was defined.

TL;DR: In this article, an approximation theorem of stochastic differential equations driven by semimartingales is proved, based on approximation of semimARTingales by a sequence of processes with piecewise monotonic sample functions.

TL;DR: In this paper, the spectral distribution of a central multivariate F matrix is shown to tend to a limit distribution in probability under certain conditions as the number of variables and the degrees of freedom tend to infinity.

TL;DR: In this paper, a stability result for sums of weighted nonnegative random variables is established and then it is utilized to obtain, among other things, a slight generalization of the Borel-Cantelli lemma and to show that the work of Jamison, Orey, and Pruitt (Z. Wahrsch. Verw. Gebiete 4 (1965), 40−44) on almost sure convergence of weighted averages of independent random variables remains valid if the assumption of independence on the random variable is replaced by pairwise independence.

TL;DR: In this article, the problem of global estimation of the mean function of a quite arbitrary Gaussian process is considered, where the loss function in estimating the function is assumed to be of the form L ( θ, a ) = ∫ [ θ ( t ) − a ( t )] 2 μ ( dt ), and estimators are evaluated in terms of their risk function (expected loss).

TL;DR: In this paper, it was shown that every full eA decomposable probability measure on Rk, where A is a linear operator all of whose eigenvalues have negative real part, is either continuous with respect to Lebesgue measure or continuous singular with respectto Lebesgege measure.

TL;DR: In this article, the general asymptotic order of magnitude for the maximal deviation of the multivariate product-limit estimate from the estimated survival function on R k is determined. But the results are not generalizable to the variable censoring model.

TL;DR: In this article, it was shown that every genuinely d-dimensional operator-self-decomposable distribution is continuous, i.e., it is continuous in the sense that

TL;DR: The concept of the inverse correlation function of a stationary process was introduced by Cleveland (Technometrics 14 (1972), 277-293) and its importance in describing the structure of a moving average of finite order h is discussed in this article.

TL;DR: The maximal correlation between a pair of σ-fields A and B becomes arbitrarily small as sup{|P ( A ⋔ B ) − P ( A ) P (B )|/[ P (A ) P(B )] 1/2, A ∈ A, B ∈ B, P ( B ) > 0, P( B )> 0} becomes sufficiently small as mentioned in this paper.

TL;DR: In this paper, a classification is given of all Gaussian measures that have the conditional independence property and such that restricted to a subspace, they coincide with a given Gaussian measure.

TL;DR: In this paper, it was shown that f(x1, x2) is TP2 for fixed correlation ϱ if and only if ϱ > 0, and if f(X1, X2)′ ∼ N(0, Σ).

TL;DR: In this paper, large-O error estimates concerning convergence in distribution as well as norm convergence for Banach space-valued martingale difference sequences are established. But these results are not applicable to the case of large numbers.

TL;DR: In this paper, the asymptotic behavior of integral kernel transformations of the multivariate empirical process is investigated when a null-hypothesis completely specifies the underlying distribution and also when parameters are also estimated from the sample.

TL;DR: In this paper, the existence of a double random integral of the form ∫ 0 1 ∫0 1 f ( s, t ) M ( ds ) M( dt ), where M (0, t ) is a stable process with independent increments is established for a wide class of functions f.

TL;DR: In this paper, the authors examined 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).

TL;DR: In this article, the notion of partial mean integrated square error is introduced and used to compare the performance of trigonometric series estimators, leading to consideration of some new estimators which have excellent properties from the points of view of both efficiency and ease of computation.

TL;DR: In this paper, a characterization of the two extreme optional increasing paths passing through a given stopping point is obtained, and a description of the largest stopping point smaller than two given stopping points is given.

TL;DR: In this article, the authors derived the equations which express zero regression from the recurrence relations of a set of special functions and used them in the proofs of the characterization theorems.

TL;DR: In this paper, it was shown that a 3 × 3 embeddable matrix P with det P ≥ 18 can be expressed as a product of at most six Poisson matrices.

TL;DR: In this paper, it was shown that the best constant in the inequality λP(supi |Xi| ≥ λ) ≤ C supiE |Zi|, for λ > 0, is C = (log 2)−1.

TL;DR: In this article, the notion of sampling for second-order q-variate processes is defined, and it is shown that if the components of a q -variate process (not necessarily stationary) admits a sampling theorem with some sample spacing, then the process itself admits a sample theorem with the same sample spacing.