Bayesian Estimation and Statistical Analysis of Risk Measurements

The Bayesian model are established for the VaR and related risk measurements. The relationship between VaR and other risk measurements including expect shortfall, tail condition expectation and conditional value at risk are discussed. Furthermore, the Bayesian estimates and Bayesian predictors of these risk measurement are derived. Thirdly, the consistency and asymptotic normality in the exponential risk model are proved. Finally, the numerical simulation method is used to verify the convergence rate under different sample sizes.     

变系数联立模型的局部线性广义矩变窗宽估计

在随机设计条件下,提出了一类变系数联立模型,运用局部线性广义矩变窗宽估计,对模型的变系数进行了估计,研究了估计量的大样本性质.利用概率论中大数定律和中心极限定理,证明了估计量的大样本性质,局部线性广义矩变窗宽估计具有相合性和渐进正态性.     

部分线性回归模型变窗宽一步局部M-估计

讨论了部分线性回归模型的变窗宽一步局部M-估计.用一步局部M-估计给出未知函数的估计,用平均方法给出参数估计.进一步通过两个引理证明一步M-估计的渐近正态性.所提出的方法继承了局部多项式的优点并且克服了最小二乘法缺乏稳健性的缺点.     

PSL（2,13）的最小级连通3度弧传递陪集图表示

通过寻找给定群G的图表示,对PSL（2,13）的连通3度弧传递陪集图表示进行研究,得到了如下结果：PSL（2,13）的最小级连通3度弧传递陪集图表示的级是182.并且给出了该陪集图表示的例子.     

随机自变量多项式回归函数的估计问题

以随机函数逼近论的观点看待统计模型问题,得到了解决其问题的具有一般性的新途径与新方法,作出了随机自变量多项式回归函数及其相应的误差方差的优良估计,其优良性的标准包括强相合性、相合渐近正态性与L1收敛性.     

随机设计非线性混合模型的统计分析

本文研究了个体观察次数为随机的非线性 混合效应模型中参数的点估计以及区间估计. 在仅给出适当的矩条件下, 给出了固定效应、随机效应的方差阵以及误差方差的矩估计, 并证明了估计量的相合性及渐近正态性. 为给出误差方差以及随机效应方差分量的置信区间, 本文也给出了误差及随机效应的四阶矩估计. 随机模拟说明了方法的有效性.     

Linear fractional composition operators on the Dirichlet space in the unit ball

We investigate the adjoints of linear fractional composition operators Cφ acting on classical Dirichlet space D(BN ) in the unit ball BN of CN , and characterize the normality and essential normality of Cφ on D(BN ) and the Dirichlet space modulo constant function D0(BN ), where φ is a linear fractional map of BN . In addition, we also show that for any non-elliptic linear fractional map φ of BN , the composition maps σ ο φ and φ ο σ are elliptic or parabolic linear fractional maps of BN .     

Normal families and fixed points of iterates

Let F be a family of holomorphic functions and suppose that there exists ε 0 such that if f ∈ F, then |(f 2 ) (ξ)|≤4-ε for all fixed points ξ of the second iterate f 2 . We show that then F is normal. This is deduced from a result which says that if p is a polynomial of degree at least 2, then p 2 has a fixed point ξ such that |(p 2 ) (ξ)|≥4. The results are motivated by a problem posed by Yang Lo.     

Infinite-dimensional 4-manifold of finite cohomological dimension under the continuum hypothesis

Under the assumption of the continuum hypothesis, a differentiable 4-manifoldM of dimension dimM=∞ and cohomological dimension cA—dimM=4 is constructed. The spaceM is perfectly normal and hereditarily separable. Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 664–670, November, 1999.     

���ڸ�ά���ݵĸ���Hotelling'sT-square ����

The paper is concerned with the two-sample mean testing problem in high-dimension settings. We propose a composite Hotelling's T-square test, establish its asymptotical normality and study its local power. The finite-sample priority of the proposed test over existing high-dimensional tests is shown by simulations and illustrated by a real data-set analysis.