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191.
Takesi Hayakawa 《Journal of statistical planning and inference》1982,6(2):105-114
Some properties of the generalized binomial coefficients and new coefficients related to symmetric functions are discussed. Several formulas of the weighted sum of invariant polynomials of two matrix arguments which are useful in multivariate distribution theory are presented. 相似文献
192.
Summary Moments and distributions of quadratic forms or quadratic expressions in normal variables are available in literature. Such
quadratic expressions are shown to be equivalent to a linear function of independent central or noncentral chi-square variables.
Some results on linear functions of generalized quadratic forms are also available in literature. Here we consider an arbitrary
linear function of matrix-variate gamma variables. Moments of the determinant of such a linear function are evaluated when
the matrix-variate gammas are independently distributed. By using these results, arbitrary non-null moments as well as the
non-null distribution of the likelihood ratio criterion for testing the hypothesis of equality of covariance matrices in independent
multivariate normal populations are derived. As a related result, the distribution of a linear function of independent matrix-variate
gamma random variables, which includes linear functions of independent Wishart matrices, is also obtained. Some properties
of generalized special functions of several matrix arguments are used in deriving these results. 相似文献
193.
黄廷祝 《电子科技大学学报(社会科学版)》1993,(2)
给出了亚(半)正定矩阵数值半径计算的一个方法,该结果与文献[1]结果的使用范围互不包含,给出了其Gerschgorin型简单实用的下界估计式,以及其它有关结果。 相似文献
194.
We consider the usual (spring balance) weighing design set-up with the design matrix having a string property meaning thereby that in every row of it, there is exactly one run of 1's (the rest of the elements being 0's). We have investigated some interesting features of such matrices and used them in deriving various optimality results. 相似文献
195.
The robust statistic T2 Dproposed by Tiku and Singh (1982) for testing the equality of mean vectors of two mu1 t ivariate populations is modified to test the equality of variance-covariance matrices. 相似文献
196.
ByoungSeon Choi 《统计学通讯:理论与方法》2013,42(8):2815-2827
It is shown that the inverse of a block Toeplitz matrix can be factored into a product of an upper block triangular, a block diagonal and a lower block triangular matrices, where the component matrices consist of the solutions of the forward and backward extended Yule-Walker equations. Also, a recursive algorithm is presented to decompose nested Toeplitz matrices, which is a generalization of the Levinson-Durbin algorithm. Its derivation is elementary. The decomposition and the algorithm are useful for solving a block Toeplitz system of simultaneous equations, particularly, which appears in the vector autoregressive moving-average model analysis. 相似文献
197.
A general formulation of the life table in the presence of individual jeterogeneity is presented. The possible effects of heterogeneity on the various life table functions are outlined. For the case of ordinary life tables, a method is presented for the evaluation of these effects. The proposed method id illustrated by a numerical example. 相似文献
198.
Hanne T. Wist 《统计学通讯:模拟与计算》2013,42(1):161-176
ABSTRACT This note discusses the approach of specifying a Gaussian Markov random field (GMRF) by the Cholesky triangle of the precision matrix. A such representation can be made extremely sparse using numerical techniques for incomplete sparse Cholesky factorization, and provide very computational efficient representation for simulating from the GMRF. However, we provide theoretical and empirical justification showing that the sparse Cholesky triangle representation is fragile when conditioning a GMRF on a subset of the variables or observed data, meaning that the computational cost increases. 相似文献
199.
C.C. aige 《统计学通讯:模拟与计算》2013,42(5):437-453
We consider the general univariate linear model E(y) = Xb, V(y) = o2 W, W symmetric nonnegative definite. A numerically stable method based on orthogonal rotations is given for computing the least squares estimate [bcirc] of b , as well as a representation of [/(b). It is shown how to extend the computations to update these results quickly and accurately when columns or rows of (y,X) are added or taken away. One of these techniques will handle the usual F-test for the general linear hypothesis, and the updating techniques can easily handle less than full rank X and W , while checking for consistency of the model. The first section describes some disadvantages of the original formulation of the problem and gives a general formulation which avoids these. The second section describes a numerically stable method for solution, while the third considers the statistical meaning of the computed quantities. Section 4 introduces the updating techniques as continuations of the original decomposition and Section 5 treats the special case of equality constraints 相似文献
200.
A peifect cell frequency is one exactly satisfying a given model General formulae foi peifect cells are provided for direct models having two Or hiee components. Foimulae are piovided for the on-diagonal cells of the corresponding hat matrices Methods for identifying outliers are discussed. 相似文献