Showing papers on "Multivariate stable distribution published in 1983"
TL;DR: In this paper, a new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions, and it is shown that such processes may arise via natural generating procedures, and that they can be approximated as closely as desired by appropriate finite models.
92 citations
TL;DR: It is shown how a multivariate empirical survivor function must be constructed in order to be considered a (nonparametric) maximum likelihood estimate of the underlying survivor function.
Abstract: This paper presents examples of situations in which one wishes to estimate a multivariate distribution from data that may be right-censored. A distinction is made between what we term 'homogeneous' and 'heterogeneous' censoring. It is shown how a multivariate empirical survivor function must be constructed in order to be considered a (nonparametric) maximum likelihood estimate of the underlying survivor function. A closed-form solution, similar to the product-limit estimate of Kaplan and Meier, is possible with homogeneous censoring, but an iterative method, such as the EM algorithm, is required with heterogeneous censoring. An example is given in which an anomaly is produced if censored multivariate data are analyzed as a series of univariate variables; this anomaly is shown to disappear if the methods of this paper are used.
89 citations
TL;DR: An analysis of the distribution of the estimates shows that they are asymptotically normal and unbiased, and that they have a variance that decreases like 1/n, n being the sample size.
Abstract: A very fast and simple algorithm for estimation of the parameters of large multivariate time series and distributed lag models is presented. An analysis of the distribution of the estimates shows that they are asymptotically normal and unbiased, and that they have a variance that decreases like 1/n, n being the sample size. The algorithm is especially applicable for estimation of large multivariate models where it is generally many times faster than maximalization algorithms.
84 citations
TL;DR: In this paper, the authors consider a multivariate Pearson family of distributions and propose a number of asymptotically efficient tests through Monte Carlo experiments, which are compared with some of the existing test procedures.
Abstract: We consider a multivariate Pearson family of distributions. Certain parametric restrictions lead to the multivariate normal distribution. Using this fact we propose a number of asymptotically efficient tests. Through Monte Carlo experiments these tests are compared with some of the existing test procedures. A table is provided from which finite-sample critical points can be obtained.
76 citations
TL;DR: A random vector is said to have a 1-symmetric distribution if its characteristic function is of the form φ(|t1| + … + |tn|) as discussed by the authors.
74 citations
TL;DR: In this article, a confidence set for the mean of a multivariate normal distribution is derived through the use of an empirical Bayes argument, which is easy to compute and has uniformly smaller volume than the usual confidence set.
Abstract: Through the use of an empirical Bayes argument, a confidence set for the mean of a multivariate normal distribution is derived. The set is a recentered sphere, is easy to compute, and has uniformly smaller volume than the usual confidence set. An exact formula for the coverage probability is derived, and numerical evidence is presented which shows that the empirical Bayes set uniformly dominates the usual set in coverage probability.
63 citations
TL;DR: In this article, the cumulative distribution function of the sumS, of correlated random variables can be obtained by considering a multivariate generalization of a gamma distribution which occurs naturally within the context of a general multivariate normal model.
Abstract: The cumulative distribution function of the sumS, of correlated random variables can be obtained by considering a multivariate generalization of a gamma distribution which occurs naturally within the context of a general multivariate normal model. By application of the inversion formula to the characteristic function of S, an accurate method for calculating the distribution of S was obtained. An explicit expression for this distribution is presented for certain parameter values in the case where the underlying multivariate normal model has the moving averages correlation structure. Agreement between the two methods was excellent.
13 citations
TL;DR: In this paper, exact and asymptotic distributions of a class of statistics whose moments are of a particular form have been obtained, and an application to Wilks's criterion for testing a linear hypothesis is given.
Abstract: In this article, exact and asymptotic distributions of a class of statistics whose moments are of a particular form have been obtained. An application to Wilks's criterion for testing a linear hypothesis is given, and it is shown by numerical comparison that the first term of the asymptotic expansion of the distribution obtained in this article is better than Box's asymptotic expansion in terms of chisquared distributions. The exact distribution is easily computable and has the distinct advantage that stable recurrence relations exist between the coefficients involved.
12 citations
TL;DR: In this article, a new expansion for the integral of the multivariate normal distribution over a region of the form (V1, m) × (uk, ∞) is given.
Abstract: Summary
A new expansion is given for the integral of the multivariate normal distribution over a region of the form (V1, m) ×.× (uk, ∞). The regions of convergence and divergence are partially identified and shown to be different from those of the tetrachoric expansion.
12 citations
TL;DR: In this paper, the authors present necessary and sufficient conditions for an invariant test to be admissible among invariant tests in the general multivariate analysis of variance problem and show that in many cases the popular tests based on the likelihood ratio matrix are inadmissible.
Abstract: Necessary and sufficient conditions for an invariant test to be admissible among invariant tests in the general multivariate analysis of variance problem are presented. It is shown that in many cases the popular tests based on the likelihood ratio matrix are inadmissible. Other tests are shown admissible. Numerical work suggests that the inadmissibility of the likelihood ratio test is not serious. The results are given for the multivariate analysis of variance problem as a special case.
8 citations
TL;DR: In this article, the authors generalize the univariate discrete exponential family of distributions to the multivariate situation and obtain recurrence relations for moments and cumulants, and the maximum likelihood estimation for the discrete exponential families.
Abstract: The paper generalizes the univariate discrete exponential family of distributions to the multivariate situation, and this generalization includes the multivariate power series distributions, the multivariate Lagrangian distributions, and the modified multivariate power-series distributions. This provides a unified approach for the study of these three classes of distributions. We obtain recurrence relations for moments and cumulants, and the maximum likelihood estimation for the discrete exponential family. These results are applied to some multivariate discrete distributions like the Lagrangian Poisson, Lagrangian (negative) multinomial, logarithmic series distributions and multivariate Lagrangian negative binomial distribution.
TL;DR: In this paper, the authors describe discrimination among multivariate autoregressive processes by the Bayes method, and the asymptotic distribution of the discriminant function and estimation of the probability of misclassification are investigated.
TL;DR: In this article, a reparametrization of the multivariate normal distribution is introduced in order to consider LR tests of significance for the hupothesis of homogeneity of relative errors, or generalized coefficients of variations.
Abstract: A reparametrization of the multivariate normal distribution is introduced in order to consider LR tests of significance for the hupothesis of homogeneity of relative errors, or generalized coefficients of variations (c. v.) θ This is in continuation of the author's results (Bennett, 1978) on tests of the equality of univariate c. v. 's from successive experiments based on a normal distribution.
TL;DR: This paper deals with the problem of identifying and testing a number of extreme sample elements as significant outliers in a sample of size n from a K-dimensional normal distribution with unknown parameters.
TL;DR: In this paper, bounds on the convergence rate of the joint distribution of order statistics to the corresponding multivariate normal distribution were derived based on the rate of convergence of the normal distribution.
Abstract: Bounds are derived on the rate of convergence of the joint distribution of order statistics to the corresponding multivariate normal distribution.
TL;DR: In this paper, the minimum variance unbiased (MVU) estimators for some multivariate normal probability models which can be found useful in the interference theory of reliability are discussed. But the MVU estimators are not considered in this paper.
TL;DR: In this article, asymptotic expansions of the null and non-null distributions of the sphericity test criterion in the case of a complex multivariate normal distribution are obtained for the first time in terms of beta distributions.
Abstract: In this paper, asymptotic expansions of the null and non-null distributions of the sphericity test criterion in the case of a complex multivariate normal distribution are obtained for the first time in terms of beta distributions. In the null case, it is found that the accuracy of the approximation by taking the first term alone in the asymptotic series is sufficient for practical purposes. In fact for p - 2. the asymptotic expansion reduces to the first term which is also the exact distribution in this case. Applications of the results to the area of inferences on multivariate time series are also given.
01 May 1983
TL;DR: In this article, an extension of Ferguson's univariate normal results for rejection of outliers is made to the multivariate case with mean slippage, and the formulation is more general than that in Schwager and Margolin and the approach is also different.
Abstract: : An extension of Ferguson's univariate normal results for rejection of outliers is made to the multivariate case with mean slippage. The formulation is more general than that in Schwager and Margolin and the approach is also different. The main result can be viewed as a robustness property of Mardia's locally optimum multivariate normal kurtosis test to detect outliers against nonnormal multivariate distributions.