Showing papers in "Journal of Multivariate Analysis in 1981"

TL;DR: The theory of elliptically contoured distributions is presented in an unrestricted setting, with no moment restrictions or assumptions of absolute continuity as mentioned in this paper, where the distributions are defined parametrically through their characteristic functions and then studied primarily through the use of stochastic representations which naturally follow from the work of Schoenberg on spherically symmetric distributions.

TL;DR: In this paper, an array of random variables (Xi,j), 1 ≤ i,j < ∞, such that permutations of rows or columns do not alter the distribution of the array, is represented as a function f(α, ξi, ηj, λi,j) of underlying iid, random variables.

TL;DR: In this article, it was shown that the empirical dependence function can be canonically separated into a finite set of independent Gaussian processes, enabling one to test the existence of dependence relationships within each subset of coordinates independently (in an asymptotic way) of what occurs in other subsets.

TL;DR: In this paper, it was shown that strong or weak convergence is possible to estimate the order of the McMillan degree of a linear system with respect to the Kronecker indices.

TL;DR: In this paper, the central limit theorem of Ibragimov for strictly stationary random sequences satisfying a mixing condition based on maximal correlations is extended to triangular arrays of random variables, and this is applied to some kernel-type estimates of probability density.

TL;DR: In this paper, a new notion of tactic for processes indexed by a directed set is introduced, and conditions under which tactics can be mapped on stopping times on the line are given.

TL;DR: In this article, the authors introduce known theory relating to the description of the set of all ARMA structures via the concept of order, n, and the coordinatisation of all structures, M(n), of given order.

TL;DR: Wei et al. as mentioned in this paper extended Hai's theorem to a more general form which unifies previous results in the literature on the strong consistency of least squares estimates in multiple regression models with nonrandom regressors.

TL;DR: In this article, the structure of full operator-stable measures was investigated on a vector group V and obtained decompositions, μ = μ1 ∗ μ2 and V = V1 ⊕ V2, in terms of the Gaussian component μ1 and the Poisson component μ2.

TL;DR: In this article, a robust principal component analysis for samples from a bivariate distribution function is described, which is based on robust estimators for dispersion in the univariate case along with a certain linearization of the bivariate structure.

TL;DR: In this article, the bounds for traces and determinants of matrices of the type X′AYY′A−1X, X′B2X(X′BCX)−1 X′C2X((X, B, C))−1) where X and Y are n × k matrices such that X′X = Y′Y = Ik and A, B and C are given matrices satisfying some conditions.

TL;DR: In this article, the almost sure convergence of the kernel-type density estimate for a strictly stationary ergodic sample is proved for a purely stationary, non-stationary, and non-correlated sample.

TL;DR: For the p -variate Poisson mean, under the sum of weighted squared error losses, weights being reciprocals of variances, a class of proper Bayes minimax estimates dominating the usual estimate, namely the sample mean is produced as discussed by the authors.

TL;DR: In this article, the authors derived conditions for the stationarity of a class of multiple autoregressive models with random coefficients, including those previously discussed by Andel ( Ann. Math. Statist. 42 (1971), 755−759; Math. Operationsforsch. Statists. 7 (1976), 735−741).

TL;DR: In this article, it was shown that in typical testing problems in multivariate exponential families, the LR test is deficient in the sense of Bahadur of order o(log n).

TL;DR: In this paper, the authors prove the global Markov property for lattice systems of classical statistical mechanics with bounded spins and finite range interactions, using a transition matrix, which together with a distribution on a hyperplane, describes completely the system.

TL;DR: In this article, an estimator is developed which incorporates a prior mean and variance for each Poisson mean estimated, which possesses substantially smaller risk than the usual estimator in a region of the parameter space and seems superior to other estimators proposed to estimate Poisson means.

TL;DR: In this paper, the authors deal with limit theorems for probabilities of large deviations for sums of independent identically distributed random vectors and give more detailed bounds for the remainder in von Bahr's limit theorem.

TL;DR: In this paper, a two-stage regression procedure is used to estimate the unknown parameters of a class of multivariate random coefficient autoregressive models and the estimates are shown to be strongly consistent and to have a distribution which converges to that of a normally distributed random vector.

TL;DR: In this article, the eigenfunctions of expectation operators of the Wishart distribution were characterized and a finite sequence of polynomial eigenspaces, EP spaces, which are invariant and irreducible under the action of the congruence transformation V → T′VT were derived.

TL;DR: In this article, the authors developed a theory of local comparison for linear rank tests of the one-sample symmetry and the k -sample problem (k ≥ 2) based on the concept of Bahadur efficiency.

TL;DR: In this article, the dependence concept of weak association is introduced and is shown to be equivalent to positive quadrant dependence, and a characterization of independence in the class of PQD random variables by means of moment conditions is proved.

TL;DR: In this article, a review of the general theory of multitype point processes is given, and spatial central limit theorems for homogeneous infinitely divisible processes are proven in Section 3.

TL;DR: In this article, a Markov's inequality for such spaces in P(X ≥ x) ≤ infG0E[g(X)]/g(x), where G0 is the class of nonnegative order-preserving functions on X such that, for each g∈G0, E[g (X)] is defined; and G1ņG0 be the subclass of concave functions.

TL;DR: This paper generalized the results of Lindley and Haitovsky for the univariate case to the multivariate normal distribution, making use of recent results in matrix algebra and generalized the efficiency lost in grouping to the multi-dimensional case.

TL;DR: In this article, a large class of multivariate densities and frequency functions, including the multivariate Poisson distribution and the compound multivariate poisson distribution, are shown to have the decreasing in transposition property introduced by Hollander, Proschan, and Sethuraman.

TL;DR: In this paper, Sarkar et al. extended this idea to cover multivariate linear regression testing problems with the same type of additional observations on a set of correlated auxiliary variables and proposed a similar test for a mean testing problem with additional observations.

TL;DR: The correspondence between Gaussian stochastic processes with values in a Banach space E and cylindrical processes which are related to them is studied and it is shown that the linear prediction and spectral measure of an E-valued Gaussian stationary process is a Gaussian random measure.

TL;DR: In this article, the authors studied the possibility of obtaining a factorization (I + a1B + … + apBp) for n-dimensional ARMA time series X(t) = [Πi=1p (I − αiB)] where B is the backward shift operator.