共查询到20条相似文献,搜索用时 15 毫秒
1.
A function f(x) defined on
=
1 ×
2 × … ×
n where each
i is totally ordered satisfying f(x y) f(x y) ≥ f(x) f(y), where the lattice operations and refer to the usual ordering on
, is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,…, Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies −DΣ−1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications. 相似文献
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Abram Kagan Paul J. Smith 《International Journal of Mathematical Education in Science & Technology》2013,44(1):91-96
Using appropriately parameterized families of multivariate normal distributions and basic properties of the Fisher information matrix for normal random vectors, we provide statistical proofs of the monotonicity of the matrix function A -1 in the class of positive definite Hermitian matrices. Similarly, we prove that A 11 < A -111, where A 11 is the principal submatrix of A and A 11 is the corresponding submatrix of A -1. These results in turn lead to statistical proofs that the the matrix function A -1 is convex in the class of positive definite Hermitian matrices and that A 2 is convex in the class of all Hermitian matrices. (These results are based on the Loewner ordering of Hermitian matrices, under which A < B if A - B is non-negative definite.) The proofs demonstrate that the Fisher information matrix, a fundamental concept of statistics, deserves attention from a purely mathematical point of view. 相似文献
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We study a multivariate extension of the univariate exponential dispersion Tweedie family of distributions. The class, referred to as the multivariate Tweedie family (MTwF), on the one hand includes multivariate Poisson, gamma, inverse Gaussian, stable and compound Poisson distributions and on the other hand introduces a high variety of new dependent probabilistic models unstudied so far. We investigate various properties of MTwF and discuss its possible applications to financial risk management. 相似文献
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An n×m real matrix A is said to be totally positive (strictly totally positive) if every minor is nonnegative (positive). In this paper, we study characterizations of these classes of matrices by minors, by their full rank factorization and by their thin QR factorization. 相似文献
6.
Friedrich Schmid 《Journal of multivariate analysis》2007,98(6):1123-1140
A new family of conditional-dependence measures based on Spearman's rho is introduced. The corresponding multidimensional versions are established. Asymptotic distributional results are derived for related estimators which are based on the empirical copula. Particular emphasis is placed on a new type of multidimensional tail-dependence measure and its relationship to other measures of tail dependence is shown. Multivariate tail dependence describes the limiting amount of dependence in the vertices of the copula's domain. 相似文献
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A new “finite section” type theorem is used to show that the members of an interesting class of bounded totally positive matrices map l∞ onto l∞ if and only if their range contains a vector which alternates in sign and has coordinates bounded away from zero. The class of matrices studied contains all banded totally positive matrices, and thus all infinite spline collocation matrices. Connections to related work and extension to matrices which are not sign regular are indicated. 相似文献
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Julius Borcea 《Transactions of the American Mathematical Society》2007,359(7):3209-3237
A notion of weighted multivariate majorization is defined as a preorder on sequences of vectors in Euclidean space induced by the Choquet ordering for atomic probability measures. We characterize this preorder both in terms of stochastic matrices and convex functions and use it to describe the distribution of equilibrium points of logarithmic potentials generated by discrete planar charge configurations. In the case of positive charges we prove that the equilibrium points satisfy weighted majorization relations and are uniquely determined by such relations. It is further shown that the Hausdorff geometry of the equilibrium points and the charged particles is controlled by the weighted standard deviation of the latter. By using finite-rank perturbations of compact normal Hilbert space operators we establish similar relations for infinite charge distributions. We also discuss a hierarchy of weighted de Bruijn-Springer relations and inertia laws, the existence of zeros of Borel series with positive -coefficients, and an operator version of the Clunie-Eremenko-Rossi conjecture.
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T. Matsunawa 《Annals of the Institute of Statistical Mathematics》1982,34(1):1-17
Summary Some criteria based on K-L information number andW-divergence are presented for a certain type of uniform approximate equivalence of two probability distributions. As applications,
some necessary and sufficient conditions are also given for the corresponding uniform asymptotic equivalence of two random
sequences.
The Institute of Statistical Mathematics 相似文献
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Javier Rojo 《Annals of the Institute of Statistical Mathematics》1996,48(2):247-255
The concepts of pure-tail orderings as defined by sq- and D-orderings are shown to order the family of reliability life distributions which age smoothly in a natural way. This ordering extends to comparisons regarding the limiting behavior of the residual life, mean residual life, sojourn time between perfect repairs in repairable systems, failure rate and, through the preservation of sq- and D-orderings by various reliability operations, to certain coherent systems of components that age smoothly. Possible applications of the results to the industrial practice of cannibalization are also noted. 相似文献
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许贵桥 《数学物理学报(A辑)》2009,29(4):1001-1011
该文考虑 Besov-Wiener 类Spqθr B(Rd)和 Spqθr B(Rd)在 Lq(Rd) 空间下 (1≤q≤ p <∞ ) 的无穷维σ -宽度和最优恢复问题.通过考虑样条函数逼近和构造一种连续样条算子, 得到了关于无穷维Kolmogorov 宽度、无穷维线性宽度、无穷维 Gel'fand 宽度和最优恢复的弱渐近结果. 相似文献
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