Showing papers in "Journal of Multivariate Analysis in 1971"

TL;DR: In this paper, a generalization of an earlier attempt by the author to obtain estimators of heteroscedastic variances in a regression model is presented, which is quite general, applicable to all experimental situations, and the computations are simple.

TL;DR: In this article, the variance of a quadratic function of the random variables in a linear model is minimized to obtain locally best unbiased estimators (MIVQUE) of variance components.

TL;DR: In this paper, the problem of estimating a linear relationship between variables which are observed with error is surveyed in various cases when additional information is available, including Wald's method, the use of instrumental variates, and the case of more than two variables.

TL;DR: In this article, it was shown that the invariant measure of the filtering process exists uniquely if and only if the stationary signal process (flow) is purely non-deterministic.

TL;DR: In this article, the singular martingales on a von Neumann algebra with respect to a given ascending sequence of Von Neumann subalgebras as functionals on the C ∗ -algebra were studied.

TL;DR: A cross section of basic yet rapidly developing topics in multivariate data analysis is surveyed, emphasizing concepts required in facing problems of practical data analysis while de-emphasizing technical and mathematical detail.

TL;DR: In this article, the authors derived exact central distributions of the extreme roots of the Wishart and MANOVA matrices and the expressions for these distributions and the associated probability integrals are written as linear combinations of the products of certain double integrals.

TL;DR: For weakly stationary stochastic processes taking values in a Hilbert space, spectral representation and Cramer decomposition are studied in this article, where necessary and sufficient spectral conditions for such stochastically processes to be purely non-deterministic are given in both discrete and continuous parameter cases.

TL;DR: The classical Kolmogorov theorem on the existence of stochastic process has been generalized in several directions following its abstract formulation by Bochner as mentioned in this paper, and a unified exposition of the key results of the existing work is given.

TL;DR: In this article, quelques conditions suffisante pour que ait un facteur indecomposable for mesures de Poisson singulieres are presented. But these conditions sont interessantes car elles s'appliquent au cas de mesures of Poisson singularus.

TL;DR: In this paper, an asymptotic expansion of the distribution of Z as well as the associated probability of misclassification with respect to the three numbers of degrees of freedom is given.

TL;DR: In this paper, the authors derived exact expressions for the joint marginal densities of any few consecutive ordered roots of a class of random matrices which includes Wishart matrix, MANOVA matrix, and canonical correlation matrix.

TL;DR: In this paper, a general method for determining the exact null density and distribution of U(p), a constant times Hotelling's generalized T02 statistic, for integral values of m ( = (n 1 − p − 1)2) is provided by inversion of Laplace transforms.

TL;DR: In this paper, a one-to-one correspondence between a quadratic function of white noise and a symmetric L 2 (R 2 ) -function is established, which is considered as an integral kernel.

TL;DR: In this article, the concepts of absolute continuity and singularity for operator-valued measures are introduced and Radon-Nikodym and Lebesgue decomposition theorems for such measures are established.

TL;DR: In this paper, the existence of a Gaussian measure W on C(0, 1]2 with covariance function W(x(s 1,t 1)·x (s 2,t 2)) =min(s1,s 2)·min(t 1, t 2 ) as its covariance functions and an extension of Donsker's theorem for C( 0, 1)2 is given.

TL;DR: In this article, it was shown that Bahadur's asymptotic representation of a sample quantile for independent and identically distributed random variables holds under certain regularity conditions for a general class of stationary multivariate autoregressive processes.

TL;DR: The conditional expectation with respect to σ-algebras on probability measure spaces has been extended for infinite measure spaces in this paper, and the existence of the conditional expectation is proved for functions in Lp with 1 ≤ p < ∞ and, for localizable measures, also in L∞.

TL;DR: In this article, nonlinear prediction theory of vector valued random variables in Orlicz spaces is presented and the results of this part are essentially best possible for these spaces, and the same ideas and methods of computation unify the otherwise almost independent parts.

TL;DR: In this article, the authors present assertions on asymptotic distributions of statistics used for the nonparametric multivariate testing symmetry under the hypothesis of symmetry H 1, the near alternative and the general alternative.

TL;DR: In this article, the quadratic form in normal vectors is denoted by XAX′ = S, where A: n × n is a symmetric matrix which is assumed to be positive definite.

TL;DR: In this paper, the asymptotic expansions for the c.d. and percentile of the statistic T = m Tr S 1 S 2 −1, where m S 1 and n S 2 are independently distributed W (m, p, Σ 1 ) and W (n, p, Σ 2 ), respectively.

TL;DR: The present paper is devoted to the study of the direct limits of direct systems of measure (resp. probability) spaces, and it is shown that the direct limit of the family ([lambda][alpha]), and if (E[alpha), [alpha], [lambda], [ lambda][alpha]) is a direct system of measure

TL;DR: In this article, the class of general incomplete multiresponse (randomized block) models, in which it is not necessary for all responses to be measured on every experimental unit, is considered.

TL;DR: In this paper, a set of functional equations for the gamma and the multivariate normal distributions were solved in terms of the Kronecker product of two matrices, and some interesting properties of this extended product along with some useful results in matrix algebra were established.

TL;DR: In this paper, it was shown that if the random vectors (X1, X2, Xn, Xm) are independent and the distribution of Y depends only on Σ j=1 n a j 2, then all Xj were independent and distributed N(0, σ).

TL;DR: In this paper, a multiplicity representation theorem for X is obtained as a result of the Hellinger-Hahn theory, and the related linear least-squares prediction problem is obtained.

TL;DR: In this paper, the authors consider the functional a(8, 6 E 0), which is linear in the sense that @) = 4&) + X2@,>, f i a function 19 = B(u), is O(u) = +9, (u) + A,&&), u E u, where A,, A, are constants.

TL;DR: In this paper, it was shown that if (X1, X8) and (X8 + 1, Xn) are two independent random vectors having a continuous joint density function which is nonzero, then they are independent and normally distributed with zero means and equal variances.