共查询到20条相似文献,搜索用时 0 毫秒
1.
B.Q. Fang 《Journal of multivariate analysis》2008,99(6):1105-1127
In this paper, the noncentral matrix quadratic forms of the skew elliptical variables are studied. A family of the matrix variate noncentral generalized Dirichlet distributions is introduced as the extension of the noncentral Wishart distributions, the Dirichlet distributions and the noncentral generalized Dirichlet distributions. Main distributional properties are investigated. These include probability density and closure property under linear transformation and marginalization, the joint distribution of the sub-matrices of the matrix quadratic forms in the skew elliptical variables and the moment generating functions and Bartlett's decomposition of the matrix quadratic forms in the skew normal variables. Two versions of the noncentral Cochran's Theorem for the matrix variate skew normal distributions are obtained, providing sufficient and necessary conditions for the quadratic forms in the skew normal variables to have the matrix variate noncentral generalized Dirichlet distributions. Applications include the properties of the least squares estimation in multivariate linear model and the robustness property of the Wilk's likelihood ratio statistic in the family of the matrix variate skew elliptical distributions. 相似文献
2.
The paper provides significant simplifications and extensions of results obtained by Gorsich, Genton, and Strang (J. Multivariate Anal. 80 (2002) 138) on the structure of spatial design matrices. These are the matrices implicitly defined by quadratic forms that arise naturally in modelling intrinsically stationary and isotropic spatial processes. We give concise structural formulae for these matrices, and simple generating functions for them. The generating functions provide formulae for the cumulants of the quadratic forms of interest when the process is Gaussian, second-order stationary and isotropic. We use these to study the statistical properties of the associated quadratic forms, in particular those of the classical variogram estimator, under several assumptions about the actual variogram. 相似文献
3.
For a normally distributed random matrix Y with mean zero and general covariance matrix ΣY and for a symmetric matrix W, necessary and sufficient conditions are derived for the Wishartness of Y′WY. 相似文献
4.
Jianhua Hu 《Journal of multivariate analysis》2008,99(3):555-571
Let Y be an n×p multivariate normal random matrix with general covariance ΣY. The general covariance ΣY of Y means that the collection of all np elements in Y has an arbitrary np×np covariance matrix. A set of general, succinct and verifiable necessary and sufficient conditions is established for matrix quadratic forms Y′WiY's with the symmetric Wi's to be an independent family of random matrices distributed as Wishart distributions. Moreover, a set of general necessary and sufficient conditions is obtained for matrix quadratic forms Y′WiY's to be an independent family of random matrices distributed as noncentral Wishart distributions. Some usual versions of Cochran's theorem are presented as the special cases of these results. 相似文献
5.
Joe Masaro 《Journal of multivariate analysis》2010,101(5):1168-1178
For a normal random matrix Y with mean zero, necessary and sufficient conditions are obtained for Y′WkY to be Wishart-Laplace distributed and {Y′WkY} to be independent, where each Wk is assumed to be symmetric rather than nonnegative definite. 相似文献
6.
Yasunori Fujikoshi 《Annals of the Institute of Statistical Mathematics》1981,33(1):279-285
Summary This paper deals with the likelihood ratio test for additional information in a multivariate linear model. It is shown that
the power of the likelihood ratio test procedure has a monotonicity property. Asymptotic approximations for the power are
also obtained. 相似文献
7.
The principal result in this paper is concerned with the derivative of a vector with respect to a block vector or matrix. This is applied to the asymptotic Fisher information matrix (FIM) of a stationary vector autoregressive and moving average time series process (VARMA). Representations which can be used for computing the components of the FIM are then obtained. In a related paper [A. Klein, A generalization of Whittle’s formula for the information matrix of vector mixed time series, Linear Algebra Appl. 321 (2000) 197-208], the derivative is taken with respect to a vector. This is obtained by vectorizing the appropriate matrix products whereas in this paper the corresponding matrix products are left unchanged. 相似文献
8.
Yoshihide Kakizawa 《Journal of multivariate analysis》2007,98(5):992-1017
Moderate deviations limit theorem is proved for quadratic forms in zero-mean Gaussian stationary processes. Two particular cases are the cumulative periodogram and the kernel spectral density estimator. We also derive the exponential decay of moderate deviation probabilities of goodness-of-fit tests for the spectral density and then discuss intermediate asymptotic efficiencies of tests. 相似文献
9.
Svetozar Kurepa 《Aequationes Mathematicae》1987,34(2-3):125-138
The present paper is related to the Jordan—von Neumann characterization of inner product spaces, to the Halperin problem concerning quadratic forms, to some results of the present author on quadratic and sesquilinear forms and to recently obtained results of C. T. Ng and of J. Vukman.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday. 相似文献
10.
11.
T. M. K. Davison 《Aequationes Mathematicae》1987,34(1):78-81
Ohne Zusammenfassung
Dedicated to Professor Otto Haupt with best wishes on his 100th birthday 相似文献
12.
Summary Schatzoff [9] obtained the forms of the probability density function (pdf) and the cumulative distribution function (cdf)
of the product of independent beta random variables when their parameters had some special values. The forms, however, did
not indicate the constants explicitly. In this paper his approach is modified so as to allow presentation of explicit expressions
for the pdf and cdf of the product of independent beta random variables (without restriction to the values of the parameters)
in neat forms. Applications in multivariate analysis are given for the central and the non-central cases.
Research supported by the National Research Council of Canada, No. A-4060. 相似文献
13.
A multivariate skew normal distribution 总被引:1,自引:0,他引:1
《Journal of multivariate analysis》2004,89(1):181-190
In this paper, we define a new class of multivariate skew-normal distributions. Its properties are studied. In particular we derive its density, moment generating function, the first two moments and marginal and conditional distributions. We illustrate the contours of a bivariate density as well as conditional expectations. We also give an extension to construct a general multivariate skew normal distribution. 相似文献
14.
The purpose of this paper is to develop compact expressions for the Fisher information matrix (FIM) of a Gaussian stationary vector autoregressive and moving average process with exogenous or input variables, a vector ARMAX or VARMAX process. We develop a representation of the FIM based on multiple Sylvester matrices. An extension of this representation yields another one but in terms of tensor Sylvester matrices. In order to obtain the results presented in this paper, the approach used in [A. Klein, G. Mélard, P. Spreij, On the resultant property of the Fisher information matrix of a vector ARMA process, Linear Algebra Appl. 403 (2005) 291-313] is extended. 相似文献
15.
Jacek Jachymski 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(3):768-774
We establish a geometric lemma giving a list of equivalent conditions for some subsets of the plane. As its application, we get that various contractive conditions using the so-called altering distance functions coincide with classical ones. We consider several classes of mappings both on metric spaces and ordered metric spaces. In particular, we show that unexpectedly, some very recent fixed point theorems for generalized contractions on ordered metric spaces obtained by Harjani and Sadarangani [J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. 72 (2010) 1188-1197], and Amini-Harandi and Emami [A. Amini-Harandi, H. Emami A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72 (2010) 2238-2242] do follow from an earlier result of O’Regan and Petru?el [D. O’Regan and A. Petru?el, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008) 1241-1252]. 相似文献
16.
17.
J. K. Ghorai 《Annals of the Institute of Statistical Mathematics》1982,34(1):467-477
Summary The results of Rosenblatt on quadratic measure of deviations of density estimates have been generalized to a wider class of
weight functions. It is pointed out that the proof of Theorem 1 of Rosenblatt is incorrect. A corrected version of the proof
is also provided. 相似文献
18.
René Blacher 《Journal of multivariate analysis》2003,87(1):2-23
We obtain the distribution of the sum of n random vectors and the distribution of their quadratic forms: their densities are expanded in series of Hermite and Laguerre polynomials. We do not suppose that these vectors are independent. In particular, we apply these results to multivariate quadratic forms of Gaussian vectors. We obtain also their densities expanded in Mac Laurin series or in the form of an integral. By this last result, we introduce a new method of computation which can be much simpler than the previously known techniques. In particular, we introduce a new method in the very classical univariate case. We remark that we do not assume the independence of normal variables. 相似文献
19.
In this paper we show how, based on a decomposition of the likelihood ratio test for sphericity into two independent tests and a suitably developed decomposition of the characteristic function of the logarithm of the likelihood ratio test statistic to test independence in a set of variates, we may obtain extremely well-fitting near-exact distributions for both test statistics. Since both test statistics have the distribution of the product of independent Beta random variables, it is possible to obtain near-exact distributions for both statistics in the form of Generalized Near-Integer Gamma distributions or mixtures of these distributions. For the independence test statistic, numerical studies and comparisons with asymptotic distributions proposed by other authors show the extremely high accuracy of the near-exact distributions developed as approximations to the exact distribution. Concerning the sphericity test statistic, comparisons with formerly developed near-exact distributions show the advantages of these new near-exact distributions. 相似文献
20.
T. Pham-Gia 《Journal of multivariate analysis》2008,99(8):1698-1716
We establish the exact expression of the density of Wilks’s statistic Λ(n,p,q), and also those of the densities of the product and ratio of two independent such statistics, in terms of Meijer functions, and provide applications with numerical illustrations in various domains of Multivariate Analysis. 相似文献