矩阵损失下随机回归系数和参数的线性估计的可容许性

§1.引言考虑一般的随机效应线性模型Y=Xβ+ε,(1.1)其中 Y 为可观测的 n 维随机向量,ε和β分别为不可观测的 n 维和 p 维随机向量,E(β)=Aα,VAR(β)=Δ≥0,E(ε)=0,VAR(ε)=V≥0,E(βε')=0,X,A,Δ和 V 分别为已知的 n×p,p×k,p×p 和 n×n 矩阵,α∈R~k 为参数。对于矩阵 B 和C,B≥C(B>C)表示 B—C 为非负定(正定)对称矩阵。     

四元数矩阵乘积的奇异值与特征值的不等式

本文给出了两个四元数矩阵乘积的奇异值的一些不等式,在此基础上估计了两个自共轭矩阵A、B的乘积的每个特征值,其中A≥0、B≥0或B>0.     

随机回归系数和参数的线性估计的可容许性的几个结果

考虑线性模型Y=Xβ+ε(1.1)其中 X 为已知的 n×p 矩阵,n≥p;β和ε分别为不可观测的 p 维和 n 维随机向量;Y是可观测的;Eβ=Aα,Eε=0,COV(?)=V,V 和 A 都已知,α∈R~k 为参数.这     

关于域上矩阵广义逆的加法映射

假设F是特征不为2的域,令Mn(F)是F上n×n矩阵的集合.本文证明了f是Mn(F)到自身的矩阵{1}-逆或{1,2}-逆的加法保持算子当且仅当f有:(a)f=0;(b)f(A)=εPAτP-1对任意A∈Mn(F),其中P∈GLn(F),τ-为域F的某个单自同态且x(1)=1,ε=±1;(c)f(A)=εP(Aτ)TP-1对于任意A∈Mn(F),其中τ,ε,P如(b)中一样意义.     

Richard模型的平均期望费用问题

设 W_t,t≥0为(Ω,■,P)上标准 Wiener 过程,■为由之所生成的上升 σ-域族,以τ_i,i≥1表任一个(?)单调上升停时列,对每个τ_i 确定一个F_(τi)可测随机变量ξ_i,我们称任一这样的对列 v={(τ_i,ξ_i),i≥1}为一脉冲过程,以 V 表脉冲过程,(以下称脉冲控制)的全体,设 h 和 B 为 R 上满足某些条件的非负实函数,再设σ,μ为任何实常数且|σ|>0.本文求得一个常数λ>0使对任一实数 x 皆有一个十分明确具体的控制 v~*={(τ_i~*,ξ_i~*),i≥1)∈V 满足lim~T→∞(1/T)E[integral from 0 to T h(x+μt+σW_t+sum τ_i~*相似文献   

非负矩阵Perron根的上下界

1.引言 本文主要讨论非负矩阵,我们将用B≥0和B>0分别表示矩阵B是非负的和正的,也就是B的每一个元素是非负的和B的每一个元素是正的.用p(B)表示方阵B的谱半径,当B≥0时,p(B)也就是B的perron根. 设(n)={1,2,…,n},A=(ai,j)是n×n非负矩阵,我们称     

矩阵损失下随机回归系数和参数的非齐次估计的可容许性

考虑线性模型 Y=Xβ+ε,Y 是可观察的 n 维向量,ε和β是不可观察的 n 维和 p 维随机向量;E(β)=Aα,VAR(β)=σ~2△≥0;E(ε)=0,VAR(ε)=σ~2V≥0;E(εβ＇)=0;X,A,△,V 皆为已知矩阵;α∈R~k,σ>0皆为未知参数,本文首次提出矩阵损失函数,并给出了(Sα,Qβ)的估计(L_1Y+α,L_2Y+b)在非齐次估计类中可容许的充要条件。     

Rasche方法在偏序集上最优停止问题中的应用

本文用Rasche方法对偏序集S中的点进行了筛选.筛选算法简单明了.设B(E)记筛选后的点集,我们证明了1)V=sup EX_τ=sup{EX_τ:τ∈B(E)};2)若最优停点存在,侧必几乎处处取值于B(E)中.     

Jörgens结果的一个新证明

文章研究有界线性算子半群的扰动问题.在一定条件下,我们表明设算子B生成最终依范连续半群S(t)(t≥τ),K是有界线性算子.如果‖ KR(σ+iτ,B)K ‖→0,τ→∞,那么算子A=B+K生成的半群T(t),t＞2τ是依范连续的.我们将此结果应用于迁移箅子,给出Jorgens结果的一个新证明.     

J(o)rgens结果的一个新证明

文章研究有界线性算子半群的扰动问题.在一定条件下,我们表明:设算子B生成最终依范连续半群S(t)(t≥τ),K是有界线性算子.如果‖ KR(σ+iτ,B)K ‖→0,τ→∞,那么算子A=B+K生成的半群T(t),t＞2τ是依范连续的.我们将此结果应用于迁移箅子,给出Jorgens结果的一个新证明.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Axiomatizability of reducts of algebras of relations

In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999.     

Lengths of periods of continued fractions of square roots of integers

Empirical study of the period’s length T of the continued fractions of $\sqrt{Q}$ (for growing integers Q) shows several strange asymptotical results, for instance, $T\leq C\sqrt{Q}\ln{Q}$ . These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers.