Showing papers in "Journal of Multivariate Analysis in 1982"

TL;DR: The Frechet distance between two multivariate normal distributions having means μX, μY and covariance matrices ΣX, ΣY is shown to be given by d2 = |μX − μY|2 + tr(ΣX + ǫ − 2(ǫ) 12) as discussed by the authors.

TL;DR: In this paper, the results of convergence by sampling in linear principal component analysis (LPCA) were derived for a random function in a separable Hilbert space, and the limiting distribution was given for the principal values and the principal factors.

TL;DR: The limit of the cumulative distribution function of the eigenvalues is determined by use of a method of moments as discussed by the authors, which is mainly combinatorial, and it is shown that the sum of eigen values, raised to k -th power, k = 1, 2, 3, 4, 5, 6, m is asymptotically normal.

TL;DR: A [phi]-entropy functional is defined on the probability space and its Hessian along a direction of the tangent space of the parameter space is taken as the metric, and the distance between two probability distributions is computed as the geodesic distance induced by the metric.

TL;DR: In this article, a multivariate generalization of the inequality for the normal distribution is presented, which is useful in solving a variation of the classical isoperimetric problem which is relevant to data compression in the theory of element identification.

TL;DR: The spectral representation theorem for stable processes linearly imbedding each symmetric stable process of index p into Lp (0 < p ≤ 2) is studied in this article.

TL;DR: In this article, the asymptotic distribution of the maximal deviation from m(x) is proved for two nonparameteric estimates of m (x): the Watson estimate when f 1 is known and the Yang estimate whenf 1 is unknown or unknown.

TL;DR: In this article, it was shown that P{supA∈a|μn(A)−μ(A)|≥e} ≤ cs(a, n2)e−2n∈2, where c is an explicitly given constant.

TL;DR: A general theory of positive dependence, which is weaker than association but stronger than orthant dependence, is developed in this paper, and the results are specialized to some concepts of a particular interest.

TL;DR: In this article, almost sure convergence properties of least-squares estimates in stochastic regression models and an asymptotic theory of related Euclidean projections are developed.

TL;DR: In this paper, the asymptotic joint distributions of certain functions of the eigenvalues of the sample covariance matrix, correlation matrix, and canonical correlation matrix in non-null situations when the population eigen values have multiplicities were derived without assuming that the underlying distribution is multivariate normal.

TL;DR: In this paper, the least absolute deviation estimates of the autoregressive constants a = (a1, …, aq) for a stationary autoregression model, were shown to have the property that Nσ(L(N) − a) converge to zero in probability, for σ < 1α, where the disturbances are i.i.d., attracted to a stable law of index α, 1 ≤ α < 2, and satisfy some other conditions.

TL;DR: In this article, it was shown that every genuinely d-dimensional distribution of class L on R d is a continuous distribution, which extends the known fact in one dimension to all finite dimensions.

TL;DR: By prescribing a pilot estimate of b* based on the same sample, Woodroofe has shown that there need be asymptotically no loss as against knowing the constant exactly, but his proposal is critically dependent on achieving a certain consistency rate for b*.

TL;DR: In this paper, the authors obtained estimates of the speed of convergence in the central limit theorem in R k for variation distance valid when (truncated) pseudo-moments are small enough.

TL;DR: In this paper, the authors compare the merits of two orthogonal series methods of estimating a density and its derivatives on a compact interval, those based on Legendre polynomials, and on trigonometric functions.

TL;DR: In this paper, the authors lay a proper foundation for studying asymptotic properties of nonhomogeneous diffusions, extending earlier criteria for transience, recurrence, and positive recurrence.

TL;DR: In this paper, it was shown that using a linear combination of linear predictors may not always be optimal and that using linear combination other that the best linear predictor may give a greater probability of correctly ordering { T i } if {( T i, x i )} are independent but not identically distributed or if the distributions are not normal.

TL;DR: In this paper, the Fourier transform from (L 2 ) B − into (l 2 ) b − is defined by ϕ(σ) = ∫ S ∗ : exp[−i ∫ R ḃ(t) Ḃ(t), dt]: b ϕb ϕdμ(B), where ϕ b denotes the renormalization with respect to ϸ� and μ is the standard Gaussian measure on the space of tempered distributions.

TL;DR: In this paper, weak consistency of b n, n ≥ 1, and associated rates of convergence under the minimal assumption that each Y n is integrable, is studied under the assumption that every Y n ∈ [1, ∈ {1, 2, 3, 4, 5, 6, 7, 8}.

TL;DR: In this paper, the authors derived asymptotic expressions for the null distributions of the likelihood ratio test statistics for multiple independence and multiple homogeneity of the covariance matrices when the underlying distributions are complex multivariate normal.

TL;DR: Finite Fourier transforms of stationary mixing processes have been shown to be asymptotically normal in quite a variety of circumstances as mentioned in this paper, including the case of a time series X(t) with t in R.

TL;DR: In this article, it was shown that the maximum likelihood estimator is inadmissible under entropy loss (EL) and squared error loss (SEL) if and only if it is admissible under SEL.

TL;DR: In this article, it was shown that Creasy's t test can be generalized to the multivariate case of a linear functional relationship, which can be used to prove the existence of linear functional relationships.

TL;DR: In this article, the authors considered the problem of estimating the mean of a multinormal random vector X with arbitrary covariance matrix V with respect to a subspace other than the origin.

TL;DR: In this article, the authors considered the problem of finding the re-descender of the distribution of X 1−θ to a sphere of radius d belonging to a specified neighborhood J of distributions spherically symmetric about 0.

TL;DR: In this paper, a set of hypothesis testing problems for the p responses q-sample model is presented, where it is a priori assumed that the response-sample interactions are null.

TL;DR: In this paper, the authors define the concept of fourth-order strong mixing rates and study their properties, and derive the condition (∗) for dependent random variables {Xa, Xa being an outcome of a local measurement upon Z. The result is applicable to point processes which admit clustering representations.

TL;DR: In this paper, a new proof of admissibility of tests in MANOVA is given using Stein's theorem, which is proved directly by means of majorization rather than by the supporting hyperplane approach.

TL;DR: In this article, Bellow and Sucheston proved that a Frechet space is nuclear if and only if every mean bounded amart is strongly a.s. convergent.