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在正态-逆Wishart先验信息下考虑多元正态线性模型Y-Nn×m(XB,In■∑)的参数矩阵B的线性假设检验问题,根据B的后验概率分布构造了关于B的两种线性假设的后验似然比检验,所得检验统计量是矩阵F-分布的特征值函数. 相似文献
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用线性贝叶斯方法去同时估计线性模型中回归系数和误差方差,并在不知道先验分布具体形式的情况下,得到了线性贝叶斯估计的表达式.在均方误差矩阵准则下,证明了其优于最小二乘估计和极大似然估计.与利用MCMC算法得到的贝叶斯估计相比,线性贝叶斯估计具有显式表达式并且更方便使用.对于几种不同的先验分布,数值模拟结果表明线性贝叶斯估... 相似文献
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在正态-逆Wishart先验下研究了多元线性模型中参数的经验Bayes估计及其优良性问题.当先验分布中含有未知参数时,构造了回归系数矩阵和误差方差矩阵的经验Bayes估计,并在Bayes均方误差(简称BMSE)准则和Bayes均方误差阵(简称BMSEM)准则下,证明了经验Bayes估计优于最小二乘估计.最后,进行了Monte Carlo模拟研究,进一步验证了理论结果. 相似文献
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针对空间变系数回归模型,通过空间加权距离构造权重矩阵,基于多元线性回归模型的贝叶斯统计推断,得到了该模型的局部线性BGWR估计方法.通过此方法推导出回归系数的后验分布,采用Gibbs抽样得到回归系数的逐点估计.将所得结果通过绘制曲面图、计算偏差均值和标准差均值与LeSage的BGWR模型估计结果进行对比,进一步说明估计方法的有效性. 相似文献
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有缺失数据的正态母体参数的后验分布及其抽样算法 总被引:1,自引:0,他引:1
在缺失数据机制是可忽略的、先验分布是逆矩阵Γ分布的假设下,利用矩阵的cholesky分解和变量替换方法,本文导出了有单调缺失数据结构的正态分布参数的后验分布形式.进-步用后验分布的组成特点,构造了单调缺失数据结构的正态分布的协方差矩阵和均值后验分布的抽样算法. 相似文献
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随机向量的t分布属于椭球等高分布族,然而,它是对称分布.在许多诸如经济学、生理学、社会学等领域中,有时回归模型中的随机误差不再满足对称性,通常表现出高度的偏态性(skewness).于是就有了偏态椭球等高分布族.本文在已有的多元偏态t分布的基础上,着重研究它的分布性质,包括线性组合分布、边缘分布、条件分布及各阶矩. 相似文献
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在线性模型中回归系数与误差方差具有正态-逆Gamma先验时,导出了回归系数与误差方差的同时Bayes估计.在均方误差矩阵准则和Bayes Pitman closeness准则下,研究了回归系数的Bayes估计相对于最小二乘(LS)估计的优良性,还讨论了误差方差的Bayes估计在均方误差准则下相对于LS估计的优良性. 相似文献
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方碧琪 《应用数学学报(英文版)》1999,15(2):220-224
1.IntrodnctionThispaperextendsthestudyofthesingularmatrixvariatebetadistributionofrank1[1]tothecaseofageneralrank.Astherelateddistributiontonormalsampling,thematrixvariatebetadistribution(alsocalledthemultivariatebetadistribution)hasbeenstudiedextens... 相似文献
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A.S. Al‐Fhaid S. Serra‐Capizzano D. Sesana M. Zaka Ullah 《Numerical Linear Algebra with Applications》2014,21(6):722-743
Let k( ? , ? ) be a continuous kernel defined on Ω × Ω, Ω compact subset of , , and let us consider the integral operator from into ( set of continuous functions on Ω) defined as the map is a compact operator and therefore its spectrum forms a bounded sequence having zero as unique accumulation point. Here, we first consider in detail the approximation of by using rectangle formula in the case where Ω = [0,1], and the step is h = 1 ∕ n. The related linear application can be represented as a matrix An of size n. In accordance with the compact character of the continuous operator, we prove that {An} ~ σ0 and {An} ~ λ0, that is, the considered sequence has singular values and eigenvalues clustered at zero. Moreover, the cluster is strong in perfect analogy with the compactness of . Several generalizations are sketched, with special attention to the general case of pure sampling sequences, and few examples and numerical experiments are critically discussed, including the use of GMRES and preconditioned GMRES for large linear systems coming from the numerical approximation of integral equations of the form (1) with and datum g(x). Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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Takeshi Izawa 《Bulletin of the Brazilian Mathematical Society》2008,39(3):401-416
For a codimension one locally-free singular holomorphic distribution, we give a residue formula in terms of the conormal sheaf
given by Pfaffian equations. We also prove a Baum-Bott type residue formula for singular distributions.
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Paola Ferrari Nikos Barakitis Stefano Serra‐Capizzano 《Numerical Linear Algebra with Applications》2021,28(1)
The singular value distribution of the matrix‐sequence {YnTn[f]}n , with Tn[f] generated by , was shown in [J. Pestana and A.J. Wathen, SIAM J Matrix Anal Appl. 2015;36(1):273‐288]. The results on the spectral distribution of {YnTn[f]}n were obtained independently in [M. Mazza and J. Pestana, BIT, 59(2):463‐482, 2019] and [P. Ferrari, I. Furci, S. Hon, M.A. Mursaleen, and S. Serra‐Capizzano, SIAM J. Matrix Anal. Appl., 40(3):1066‐1086, 2019]. In the latter reference, the authors prove that {YnTn[f]}n is distributed in the eigenvalue sense as under the assumptions that f belongs to and has real Fourier coefficients. The purpose of this paper is to extend the latter result to matrix‐sequences of the form {h(Tn[f])}n , where h is an analytic function. In particular, we provide the singular value distribution of the sequence {h(Tn[f])}n , the eigenvalue distribution of the sequence {Ynh(Tn[f])}n , and the conditions on f and h for these distributions to hold. Finally, the implications of our findings are discussed, in terms of preconditioning and of fast solution methods for the related linear systems. 相似文献
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Paolo Tilli 《Linear and Multilinear Algebra》2013,61(2-3):147-159
An elementary and direct proof of the Szegö formula is given, for both eigen and singular values. This proof, which is based on tools from linear algebra and does not rely on the theory of Fourier series, simultaneously embraces multilevel Toeplitz matrices, block Toeplitz matrices and combinations of them. The assumptions on the generating function f are as weak as possible; indeedf is a matrix-valued function of p variables, and it is only supposed to be integrable. In the case of singular values f(x), and hence the block p-level Toeplitz matrices it generates, are not even supposed to be square matrices. Moreover, in the asymptotic formulas for eigen and singular values the test functions involved are not required to have compact support. 相似文献
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研究了一类具分布时滞的广义系统模型,用矩阵测度和Krasnoselskii不动点定理获得了其周期解存在的若干充分条件,并举例说明其应用. 相似文献
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THE ASYMPTOTIC SOLUTION FOR A CLASS OF SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR SINGULAR EQUATION
The singularly perturbed boundary value problem for a class of semilinearsingular equation is considered. Using a simple and special method the asym-ptotic behavior of solution is studied. 相似文献
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Aubin Arroyo 《Bulletin of the Brazilian Mathematical Society》2007,38(3):455-465
In the context of Cr-flows on 3-manifolds (r ≥ 1), the notion of singular hyperbolicity, inspired on the Lorenz Attractor, is the right generalization of hyperbolicity
(in the sense of Smale) for C1-robustly transitive sets with singularities. We estabish conditions (on the associated linear Poincaré flow and on the nature
of the singular set) under which a transitive attractor with singularities of a C2-flow on a 3-manifold is singular hyperbolic. 相似文献
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H-矩阵的实用判定及谱分布 总被引:2,自引:0,他引:2
1引言及记号因为非奇异H-矩阵主对角元非零,所以本文总假定所涉及矩阵主对角元非零,并且设A=(aij)∈Cn×n为n阶复方阵,N={1,2,…,n}.记N1={i∈N |Pi(A)<|aii|Pi(A)}, N4={i∈N | |aii|≥Pi(A)>Ri(A)}, N5={i∈N | |aii|>Pi(A)=Ri(A)},N0={i∈N | |aii|≤Ri(A),|aii|≤Pi(A)},即N=N1∪N2∪N3∪N4∪N5∪N0. 相似文献