Search

Abstract In this paper a likelihood ratio test is developed through matrix projections for the hypothesis on the homogeneity of mean vectors in MANOVA. It is assumed that the mean vectors are under a general multivariate order restriction. The multivariate order relation in the restriction is a generalization of orders in real numbers. Based on the study of the structure of the acceptance region with respect to a mirror image transformation, and the properties of transformed matrix distributions, the unbiasedness of the test is established. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose one new alternative formula for moment generating function of random vectors via the inverse survival function. A recursive formula for moment generating function of random vector is obtained and as application, we derive the corresponding alternative formula for mixed moment. Several examples are also presented along with the theory. [ABSTRACT FROM AUTHOR]

Abstract Let us consider a discrete-time n -dimensional stochastic process z , with components x = (x 1 , … , x m 1 ) ′ and y = (y 1 , … , y m 2 ) ′ , m 1 + m 2 = n. We want to study causality relationships between the variables in x and y. Suppose that we find that y Granger causes x. Then we would expect to be able to pick out at least one of these variables, say y j , having a causal impact on x. It turns out that, when we consider the conditioning information set defined by the past observations of x and all the y i , i ≠ j , it may be that y j has no causal impact on x , irrespective of the particular j = 1 , 2 , … , m 2 that we tried to pick out. This is a puzzling property. The paper provides a condition under which this property cannot hold. [ABSTRACT FROM AUTHOR]

Consider a random sample of n independently and identically distributed p -dimensional normal random vectors. A test statistic for complete independence of high-dimensional normal distributions, proposed by Schott (2005), is defined as the sum of squared Pearson’s correlation coefficients. A modified test statistic has been proposed by Mao (2014). Under the assumption of complete independence, both test statistics are asymptotically normal if the limit lim n → ∞ p ∕ n exists and is finite. In this paper, we investigate the limiting distributions for both Schott’s and Mao’s test statistics. We show that both test statistics, after suitably normalized, converge in distribution to the standard normal as long as both n and p tend to infinity. Furthermore, we show that the distribution functions of the test statistics can be approximated very well by a chi-square distribution function with p ( p − 1 ) ∕ 2 degrees of freedom as n tends to infinity regardless of how p changes with n . [ABSTRACT FROM AUTHOR]

For a sequence { X n , n ≥ 1 } of coordinatewise asymptotically almost negatively associated random vectors in Hilbert space, we investigate the convergence of ∑ n = 1 ∞ 1 n 1 + α E ( max 1 ≤ k ≤ n ‖ S k ‖ − ϵ n α ) + and ∑ n = 1 ∞ log n n 1 + α E ( max 1 ≤ k ≤ n ‖ S k ‖ − ϵ n α ) + , where S k = ∑ i = 1 k X i and a + = max { a , 0 } . This investigation provides the complete moment convergence for the case α r = 1 . [ABSTRACT FROM AUTHOR]

In this letter we derive the multivariate Stein’s lemma for truncated elliptical random vectors. The results in this letter generalize Stein’s lemma for elliptical random vectors given in Landsman and Nešlehová (2008), and the tail Stein’s lemma given in Landsman and Valdez (2016). We give a conditional Stein’s-type inequalities and a conditional version of Siegel’s formula for the elliptical distributions, and by that we generalize results obtained in Landsman et al. (2013) and in Landsman et al. (2015). Furthermore, we show applications of the main results in the letter for risk theory. [ABSTRACT FROM AUTHOR]

This article provides necessary and sufficient conditions that characterize independence among sub-vectors of a singular multivariate skew-normal random vector. [ABSTRACT FROM AUTHOR]

This paper presents a new investigation to the connections among the ordinary least squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of the whole and partial mean parameter vectors in a multiple partitioned linear model. We first give some general results on the equivalence of the OLSEs and the BLUEs under a general linear model, and derive some new facts on the connections among the OLSEs and the BLUEs of the whole and partial mean parameter vectors in the model. [ABSTRACT FROM AUTHOR]

In this paper, we discuss stochastic comparisons of lifetimes of parallel and series systems with independent heterogeneous Birnbaum–Saunders components with respect to the usual stochastic order based on vector majorization of parameters. Specifically, let X 1 , … , X n be independent random variables with X i ∼ B S ( α i , β i ) , i = 1 , … , n , and X 1 ∗ , … , X n ∗ be another set of independent random variables with X i ∗ ∼ B S ( α i ∗ , β i ∗ ) , i = 1 , … , n . Then, we first show that when α 1 = ⋯ = α n = α 1 ∗ = ⋯ = α n ∗ , ( β 1 , … , β n ) ⪰ m ( β 1 ∗ , … , β n ∗ ) implies X n : n ≥ s t X n : n ∗ and ( 1 β 1 , … , 1 β n ) ⪰ m ( 1 β 1 ∗ , … , 1 β n ∗ ) implies X 1 : n ∗ ≥ s t X 1 : n . We subsequently generalize these results to a wider range of the scale parameters. Next, we show that when β 1 = ⋯ = β n = β 1 ∗ = ⋯ = β n ∗ , ( 1 α 1 , … , 1 α n ) ⪰ m ( 1 α 1 ∗ , … , 1 α n ∗ ) implies X n : n ≥ s t X n : n ∗ and X 1 : n ∗ ≥ s t X 1 : n . Finally, we establish similar results for the log Birnbaum–Saunders distribution. [ABSTRACT FROM AUTHOR]

Let X be a max-stable random vector with positive continuous density. It is proved that the conditional independence of any collection of disjoint subvectors of X given the remaining components implies their joint independence. We conclude that a broad class of tractable max-stable models cannot exhibit an interesting Markov structure. [ABSTRACT FROM AUTHOR]

This note establishes the weak law of large numbers for sums of negatively associated random vectors in Hilbert spaces. Illustrative examples are provided, one of which shows that the conditions for the weak law of large numbers cannot be dispensed with. [ABSTRACT FROM AUTHOR]

When data come from a mixture of two weakly symmetric distributions with different means and proportional covariances, we estimate the best linear discriminant projection with the projection of the standardized data onto the direction of a vector-valued measure of skewness. [ABSTRACT FROM AUTHOR]

Let (ξ1,η1),(ξ2,η2),... be a sequence of i.i.d. two-dimensional random vectors. We prove a functional limit theorem for the maximum of a perturbed random walk max0≤k≤n(ξ1+...+ξk+ηk+1) in a situation where its asymptotics is affected by both max0≤k≤n(ξ1+...+ξk) and max1≤k≤nηk to a comparable extent. This solves an open problem that we learned from the paper "Renorming divergent perpetuities" by P. Hitczenko and J. Wesołowski. [ABSTRACT FROM AUTHOR]

Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement beyond the unstructured Rosenthal inequality of quadratic forms when dimension of the vectors increases without bound. Applications to test the block diagonal structures and detect the sparsity in the high-dimensional covariance matrix are presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a framework of risk measures for portfolio vectors, which is an extension of the ones introduced by Burgert and Rüschendorf (2006) and Rüschendorf (2013). Representation results for coherent and convex risk measures for portfolio vectors are provided. Applications to the multi-period risk measures are also given. [Copyright &y& Elsevier]

Abstract: We prove the Kahane contraction principle for the tail probabilities of linear combinations of a finite exchangeable system of random variables. Our note goes back to the maximum inequalities for permutations developed by Steinitz, Garsia, Nikishin, Maurey and Pisier, and Kashin having applications in analysis and function theory. The result seems to be new, even in the case of reals. [Copyright &y& Elsevier]

In this paper, we determine the exact distribution of the vector of the componentwise maximum of two absolutely continuous dependent random vectors and we show that it is a finite mixture of particular skew distributions studied in the literature. The results are detailed when the two vectors are elliptically distributed and some particular cases are discussed. The exact expression of the covariance matrix is obtained in the normal case. [ABSTRACT FROM AUTHOR]