Showing papers in "Journal of Multivariate Analysis in 1979"

TL;DR: In this article, expressions describing the asymptotic behavior of the bias and variance of k-nearest neighbor density estimates with weight function w are obtained under appropriate assumptions, and the behavior of these estimates is compared with that of kernel estimates.

TL;DR: The strong consistency of least squares estimates in multiple regression models with independent errors is obtained under minimal assumptions on the design and weak moment conditions on the errors.

TL;DR: In this paper, a unified theory for the estimation of ∑ and ∑−1 is proposed, which is based on the dominance results of the Wishart distribution with unknown matrix Σ and k degrees of freedom.

TL;DR: In this paper, a class of random variables X sub 1, 1,..., X sub n are defined to have a joint distribution with Weibull minimums after arbitrary scaling if minimum over i of (a sub i) has a one dimensional weibull distribution for arbitrary constants a sub i 0, i = 1, n.

TL;DR: In this article, the authors define stable distributions as those having a domain of attraction, where vectors are used for normalization, and their domains of attraction are given in a number of equivalent forms.

TL;DR: In this paper, separation theorems for singular values of a matrix, similar to the Poincare separation theorem for the eigenvalues of a Hermitian matrix, are proved.

TL;DR: The limit theorems for polylinear forms are obtained in this paper, where conditions are found under which the distribution of the polylinear form of many random variables is essentially the same as if all the distributions of arguments were normal.

TL;DR: In this paper, strong invariance principles for the latter and also for appropriate functionals of it are established for distribution-free tests of independence based on a multivariate empirical process.

TL;DR: In this article, the problem of estimating the mean when n observations X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14, X15, X16, X17, X18, X19, X20, X21, X22, X23, X24, X25, X26, X27, X28, X30, X31, X32, X33, X34, X35,

TL;DR: In this paper, three methods of estimating the parameters of a power spectrum are analyzed and three methods are shown to give consistent and, under certain conditions, asymptotically equivalent results.

TL;DR: In this paper, the first occurrence of elements in a finite set with k elements was studied with respect to the stochastic process of fair coin-tossing and the results provided a better and deeper understanding of the fair coin tossing process.

TL;DR: In this paper, nonparametric estimation of the (vector of) intercept following a preliminary test on the regression vector is considered, along with the asymptotic distribution of these estimators.

TL;DR: In this article, the structure of the nonlinear space of a spherically invariant process is studied and the problem of discriminating between two SPs as well as nonlinear estimation for SPs is solved.

TL;DR: In this paper, the authors considered the maximum likelihood estimation of the five parameters of a linear structural relationship y = α + βx when α is known, and the parameters are β, the two variances of observation errors on x and y, the mean and variance of x.

TL;DR: In this article, the concept of a semi-martingale is extended to processes with index set in the plane, and sufficient conditions for a Doob-Meyer decomposition are obtained, and a maximal inequality and almost everywhere convergence theorem is given for planar Semi-Martingales in LlogL.

TL;DR: In this paper, the authors obtained asymptotic expressions for the joint distributions of certain functions of the eigenvalues of the Wishart matrix, correlation matrix, MANOVA matrix and canonical correlation matrix when the population roots have multiplicity.

TL;DR: In this article, the authors extend the result in several ways: they consider nets of not necessarily finite partitions, they consider spaces LEp(μ) of vector valued pth power Bochner integrable functions, and they characterize relatively strong compact sets K in LEp (μ) by means of uniform strong convergence Eπf → f.

TL;DR: In this article, it is shown that L∞ is the smallest subclass of L0 with the closure properties above containing all the stable measures, which is analogous to those defined earlier by K. Urbanik on the real line and studied by him and by the authors.

TL;DR: In this article, asymptotic expansions for the non-null distributions of certain test statistics concerning a correlation matrix in a multivariate normal distribution are given for the distribution of a function of the sample correlation matrix.

TL;DR: In this article, the probability generating function (pgf) of an n-variate negative binomial distribution is defined to be [β(s1,…,sn)]−k where β is a polynomial of degree n being linear in each si and k > 0.

TL;DR: In this article, a third-order optimum property of the maximum likelihood estimator is extended to not necessarily symmetric loss functions under an appropriate restriction on the class of competing estimators.

TL;DR: In this paper, a necessary and sufficient condition for the weak convergence of uniform measures on an arbitrary Hausdorff uniform space in terms of their projections in metric spaces is presented.

TL;DR: In this paper, a linear filtering problem is formulated and its solution in terms of the coefficients of the analytic function which factorizes the spectral distribution of the known data and the coefficients which describe the cross correlations is given.

TL;DR: In this article, it was shown that f ( p ) are uniformly strongly consistent estimators of f (p ), the p th order derivative of f, if and only if f(p ) is bounded and uniformly continuous.

TL;DR: In this paper, it was shown that the conditional distribution of the first p components of a normalized sum of i.i.d. m -dimensional random vectors, given the complementary subvector, admits a Chebyshev-Cramer asymptotic expansion of order o(n −(s−2) 2 ), uniformly over all Borelsets in R p and uniformly in a region of the conditioning subvector that includes moderate deviations.

TL;DR: In this article, uniform and non-uniform Berry-Esseen bounds for strongly mixing and uniformly mixing stationary sequences of random vectors are given based on the classical Bernstein procedure, and the proofs are shown in Table 1.

TL;DR: In this article, a simple branching diffusion process is given as an elementary model of spatial evolution, and a parametric estimation theory is presented for this model, where a spatial central limit theorem and spatial strong law of large numbers are also obtained.

TL;DR: In this article, asymptotic expansions for the multivariate noncentral F distribution and for the distribution of latent roots in MANOVA and discriminant analysis are given for large error degrees of freedom.

TL;DR: In this paper, the authors extend the notion of real-valued asymptotic martingales to the Banach lattice valued case, and prove that a quasi-interior point in the dual is an l 1 ( Γ ) point.

TL;DR: For discrete and continuous time Markov processes whose state space is a set of measures, laws of large numbers, central limit theorems, and laws of the iterated logarithm are obtained as discussed by the authors.