Vec and vech operators for matrices,with some uses in jacobians and multivariate statistics

The vec of a matrix X stacks columns of X one under another in a single column; the vech of a square matrix X does the same thing but starting each column at its diagonal element. The Jacobian of a one-to-one transformation X → Y is then ∣∣?(vecX)/?(vecY) ∣∣ when X and Y each have functionally independent elements; it is ∣∣ ?(vechX)/?(vechY) ∣∣ when X and Y are symmetric; and there is a general form for when X and Y are other patterned matrices. Kronecker product properties of vec(ABC) permit easy evaluation of this determinant in many cases. The vec and vech operators are also very convenient in developing results in multivariate statistics.     

一个新的增算子不动点定理

本文在新的条件下，证明了增算子不动点的存在性．     

Asymptotic distributions of functions of a sample covariance matrix under the elliptical distribution

This paper is concerned with asymptotic distributions of functions of a sample covariance matrix under the elliptical model. Simple but useful formulae for calculating asymptotic variances and covariances of the functions are derived. Also, an asymptotic expansion formula for the expectation of a function of a sample covariance matrix is derived; it is given up to the second-order term with respect to the inverse of the sample size. Two examples are given: one of calculating the asymptotic variances and covariances of the stepdown multiple correlation coefficients, and the other of obtaining the asymptotic expansion formula for the moments of sample generalized variance.     

Kronecker积AB的广义逆的表示及其应用

本文给出矩阵A和B的Kronecker积的加权Moore－Penrose逆、Drazin逆和群逆的表示，并应用这些结果给出投影算子AAMN，AMNA，AdA和AgA的行列式表示，已知的关于Moore－Penrose逆和正则逆的结果，均为本文的特例．     

一类线性偏微分算子的亚椭圆性

利用拟微分算子研究了一类线性偏微分算子的亚椭圆性,得到了 Sobolev 空间范数的估计,从而得出了该类算子具有亚椭圆性的充分条件。     

附加噪声长记忆过程的半参数估计方法研究

附加噪声长记忆过程的参数估计在实证研究中一直受到回避.本文通过聚合算子对样本数据进行降噪处理,研究了局部Whittle(LW)估计和对数周期图(LP)回归两种半参数估计方法.结果表明LW估计方法相比LP回归,解决了半参数方法的参数选取问题,且能够完全忽略噪声数据的影响而得到一致的估计.将LW估计应用于中国股市,发现重大突发事件发生时的长记忆性表现得最为强烈,且事件后比事件前要强烈.     

网络融合下基于运营服务的企业竞争力提升

结合企业竞争力和网络融合理论,对网络发展新时期的企业竞争力进行分析和讨论,提出网络融合背景下企业新竞争力要素以及竞争力指标体系,并对该企业指标体系进行物元模型建立及可拓学评价分析,得出的融合背景下最优化提升企业竞争力的运营及服务的方法,有助于信息运营商提升企业竞争力和改善企业管理服务。     

国内电信运营商品牌整合研究

当前,随着国内电信业完成重组,在3G牌照的发放和三网融合的背景下,中国电信业进入了全业务运营时代,由两家寡头垄断变成三家竞争,竞争进一步加剧。三大运营商目前的品牌体系较为庞大和复杂,且没有推出融合的品牌。在世界电信行业的开放和电信业务的渗透与融合下,国外电信运营商大多通过整合品牌和拓展市场来提高核心竞争力。基于此,通过对国内电信运营商的品牌现状和品牌整合必要性的分析,再借鉴国外运营商品牌整合的成功经验,为三大运营商提出了相应的建议和对策。     

特殊无穷维矩阵Hamilton算子的探讨

本文在原有标量Hamilton算子的基础上,分别构造且证明了三类不同阶数的矩阵Hamilton算子的形式,并得到这些算子与已给定的Hamilton算子形成了三个特殊Hamilton算子对的结论.     

Local Convergence Rate of Mean Squared Error in Density Estimation

The local convergence rate of a multivariate density estimators based on the certain delta-sequence is studied. In contrast to known results, the conditions on the density are formulated in terms of the modulus of continuity. The main contribution of this study is relaxing the corresponding smoothing conditions in terms of arbitrary modulus of continuity type majorant. In particular, when the density f ∈ L ^p (R ^d ) satisfies Lipschitz condition of order γ = 1 at x, the rate of convergency contains terms with logarithm, which is the best possible convergency rate.