Showing papers in "Journal of Multivariate Analysis in 1980"

TL;DR: In this article, a function f(x) defined on X = X 1 × X 2 × × × X n where each X i is totally ordered satisfying f (x ∨ y) f(xi ∧ y) ≥ f(y) f (y), where the lattice operations ∨ and ∧ refer to the usual ordering on X, is said to be multivariate totally positive of order 2 (MTP2).

TL;DR: In this paper, the reverse generalized correlation inequality P{ai ≤ Xi ≤ bi, i ∈ I, Xν ≤ bν, ν ∈ K, where I, J and K denote the set of indices {1,…, k}, {k + 1, ǫ, k + l], {k+ l + n, Ãǫ, Ã Ã n} for any set of PF2 functions {ϕv} (i.e.

TL;DR: For any class Q of distributions on Rd, let L(Q) be the class of limit distributions of bn−1(X1 + … + Xn) − an, where {Xn} are independent Rd-valued random variables, each with distribution in Q, bn > 0, an ∈ Rd, and {bn−1Xj} is a null array as discussed by the authors.

TL;DR: In this paper, the asymptotic properties of a vector ARMAX system are considered under general conditions, relating to the nature of the exogenous variables and the innovation sequence and to the form of the parameterization of the rational transfer functions, from exogenous variable and innovations to the output vector.

TL;DR: The results on asymptotically Bayes risk efficient classification to the general regression scenario are extended and Lp consistent estimators for an arbitrary regression function provided only that the dependent variable has a finite absolute pth moment are found.

TL;DR: In this article, the authors studied the asymptotic behavior of the solution of a bilinear stochastic evolution equation for large times and established conditions for the existence of a stationary random field.

TL;DR: In this article, two generalizations of the Brunn-Minkowski inequality for convex sets are presented along with their direct and simple proofs, and the connection between Anderson's inequality and these inequalities are discussed.

TL;DR: In this paper, the Grassmann manifold of r-subspaces in R n invariant under the group of rotations of R n has been studied, where the conditional probability measure of ω given ω is uniform on the boundary of the unit (n − r)-ball in ω⊥ with centre at the origin.

TL;DR: In this article, the asymptotic null distribution of a weighted Cramer-von Mises type test for independence was obtained by using approximate Bahadur slopes to find good weight functions for certain alternatives.

TL;DR: In this paper, the authors consider an incomplete Dirichlet integral of type I with several interesting applications connected with the multinomial distribution and provide tables of this integral along with other useful tables.

TL;DR: In this paper, the authors examined the convergence properties of the tetrachoric series and established the following: for orthant probabilities, the TRS converges if |;ϱij|; 1(k − 1) or k is odd and ϱij > 1 (k − 2), 1 ≤ i < j ≤ k.

TL;DR: In this article, the inverted complex Wishart distribution and its use for the construction of spectral estimates are studied and the density, some marginals of the distribution, and the first and second-order moments are given.

TL;DR: In this paper, it was shown that if r(t) log t → 0 as t → ∞, the time and space-normalized point process of a Gaussian process of exits converges in distribution to a Poisson process on the unit cylinder, and that the points in R3 generated by the local e-maxima of χ2(t)-process converges to a poisson process in R 3 with intensity measure (in cylindrical polar coordinates) (2πr2)−1 dt dθ dr.

TL;DR: In this article, it was shown that the usual invariant normal-theory tests are exactly robust for both the null and non-null cases, under a wider class of distributions for which the vector observations are not necessarily either Gaussian or independent.

TL;DR: In this article, the authors derived maximum likelihood estimators (MLEs) for parameters in a much more general model, and several special cases including the multivariate linear functional relationship model are discussed.

TL;DR: In this article, it was shown that if an operator-stable distribution on Rn has n linearly independent univariate stable marginals, then its exponents are semi-simple operators.

TL;DR: In this article, a general class of estimators dominating the minimum variance unbiased estimator (MVUE) or an estimator which is a known constant multiple of the MVUE is produced under different weighted squared error losses.

TL;DR: In this article, the authors considered situations in which independent structurally identical decision problems are to be faced either simultaneously or serially, and provided decision rules for finite state components simultaneously admissible and satisfying the strengthened optimality property.

TL;DR: In this article, the robustness of the standard likelihood ratio test (LRT) under the multivariate normal regression model and also the inference robustness under the univariate set up are established for certain nonnormal distributions of errors.

TL;DR: In this paper, the large sample null distribution of a progressively censored nonparametric test for multiple regression proposed by Majumdar and Sen is computed and compared with the power of the corresponding fixed sample tests.

TL;DR: It is shown that the capacity of the Gaussian channel can be achieved by transmitting a Gaussian message and using additive linear feedback, and given in terms of the covariance functions of the input processes.

TL;DR: In this article, some of the familiar transformations of r are examined for their robustness to non-normality and the effects of nonnormality are assessed through the parameters μ′1, μ2, γ1, and γ2.

TL;DR: In this paper, a general model for (nonsequential) statistical decision theory, which extends Wald's classical model, is presented, and a general theorem on the existence of admissible nonrandomized Bayes rules is derived.

TL;DR: In this paper, two test statistics based upon the empirical characteristic function are proposed and the limiting distributions of these test statistics are obtained and methods are suggested for using these limiting distributions to calculate critical regions.

TL;DR: In this paper, some fundamental properties of the empirical distribution functions are derived in the case of mixing random variables, and these properties are then utilized to study asymptotic normality and strong laws of large numbers for functions of order statistics.

TL;DR: In this article, it was shown that U : E → F is an Asplund operator and UX n is a weak sequential potential of class (B) in E, then UX n converges to 0 weakly in F almost everywhere.

TL;DR: In this paper, it is shown that the estimate mn(X) = Σi = 1n wniYi∗Σi= 1n Wni of m(X), = E{Y|X|X} satisfies E{|mn(X)-m(X)|p} 0 (p ≥ 1) whenever E{ |Y|p} < ∞, ln∞, and the triangular array of positive weights {wni} satisfies supi ≤ nwniΣI = 1 n wni 0.

TL;DR: In this article, the authors generalized Levy's second theorem and obtained a new characterization of Levy probability distribution functions on Euclidean spaces, which was used to obtain a new characterisation of operator stable distribution functions and to show that symmetric Levy distribution functions need not be symmetric unimodal.

TL;DR: In this article, it is suggested to replace A by B′B, where B is allowed to vary freely, subject possibly to BX = 0, subject to AX = 0.

TL;DR: In this paper, the Lindberg-Levy method was used to estimate the expected value of a class of smooth functions (f ∈ C r (R )) of the normalized partial sums of dependent random variables by the expectation of the corresponding functions of normal random variables.