Sβ不可估时（Sβ,σ^2）的联合估计的可容许性

对于一般的Ｇ－Ｍ模型Ｙ－Ｎ（Ｘβ，σ＾２Ｖ），Ｖ≥０，当Ｓβ不是线性可估的时，本文分别得到了矩阵损失下（Ｓβ，σ＾２）的联合估计（ＬＹ＋ａ．ＹＡＹ）的估计类中和在一切估计的类中可容许的充要条件，以及在二次损失ＬＹ＋ａ－Ｓβ＋（ＹＡＹ－σ＾２）＾２下和估计类中可容许的充要条件。     

在一般Gauss─Markoff模型下线性变换保最佳线性最小偏倚估计

在一般Ｇａｕｓｓ－Ｍａｒｋｏｆｆ模型｛Ｙ，Ｘβ，Ｖ｝下，设Ｆ是一个适当阶矩阵，Ｃ为任意适当维向量，本文找到了ＡＹ是Ｃ＇β的最小偏倚估计的充分必要条件及ＡＹ是Ｃ＇β的最佳线性最小偏倚估计的充要条件．在以概率１意义下，证明了对于所有适当维向量Ｃ，Ｃ＇β的最佳线性最小偏倚估计能被表示成ＦＹ的线性函数的充要条件，且在此条件下，线性变换保最佳线性最小偏倚估计．     

利用非负约束主成份分析得出的一个解决校准统计问题的新方案

本文对多维（Ｐ维）校准统计问题：Ｙｉ～Ｎｐ（αｘｉ＋β，Σ），利用主成份分析和非负约束规划的方法将原用反映指标向量Ｙ０估计相应之Ｘ０变为只用一个综合指标去估计Ｘ０，使多维校准问题降格成单维情况。（这里Ｙｉ和Ｙ０即反映指标向量，如α，β一样都是Ｐ维向量）     

多元线性模型参数的预检验估计

本文对于多元线性模型Ｙ～（ＸＢ,Σ＠Ｉｎ）提出参数Ｂ一种预检验估计方法当Σ已知时,给出一种整洁有偏估计,得到了它在均方误差（阵）准则下优于ＢＬＵＥ的充要条件当Σ未知时,提出一种非线性两步估计,并得到它的精确均有误差阵结果和优于ＢＬＵＥ的充要条件本文还给出估计占优条件的检验统计量     

部分线性模型参数分量的L_1模估计的渐近正态性

考虑ｉ．ｉ．ｄ．观测数据（Ｔ１，Ｘ１，Ｙ１），…，（Ｔｎ，Ｘｎ，Ｙｎ），其中Ｔｉ∈［０，１］，ｕｉ为观测误差，β０为未知参数向量，ｇ０为未知函数．本文用分段多项式ｇｎ（ｔ）来逼近ｇ０（ｔ），求解得到β０的估计β和ｇ０的估计ｇｎ，其中ｎ是一个ｍ阶分段多项式类．在一定条件下，本文证明了渐近正态．     

全局最优信息融合估计算法(Ⅱ)

假定局部滤波器的状态估计是相关的条件下，得到了状态向量的全局最优融合估计，作为应用，得到了比文[1]中更为普遍，实用的结果。     

条件中位数L_1－模核估计的逐点相合性

设（Ｘ，Ｙ）．（Ｘ１，Ｙ１），（Ｘ２，Ｙ２），…为Ｒｄ×Ｒ１上ｉ．ｉ．ｄ．随机向量序列。Ｙ对Ｘ的条件中位数θ（ｘ）定义为在Ｘ＝ｘ时Ｙ的条件分布函数的中位数．校函数Ｋ（·）是Ｒｄ上正实值函数，对ｘ∈Ｒｄ，θ（ｘ）的Ｌ１－模核估计θｎ（ｘ）定义由（１）给出．本文中，我们将文献［４］的均匀核法推广至一般核的情况，并在定义了θ的Ｌ１－模核估计基础之上，研究了其逐点相合性质．     

协方差改进估计与相依混合效应回归方程

本文首先讨论了广义线性模型Ｙ＝Ｘβ＋ε（ε～（Ｏ，Ｖ））的系数β的最优线性无偏估计是用Ｔ２＝ＸＹ作为伴随变量对最小二乘估计Ｔ１＝（ＸＸ）－１Ｘ１Ｙ进行改进而得到的协方差改进估计．并把所得结果用于经济领域中的线性相依回归方程系统（ＳｅｅｍｉｎｇｌｙＵｎｒｅｌａｔｅｄＲｅｇｒｅｓｓｉｏｎＥｑａｕｔｉｏｎｓＳｙｓｔｅｍ）．然后关于一类线性相依混合效应回归方程系统，提出了一种优化估计方法。     

关于广义Stein估计的注记

对于一般的正态线性回归模型Ｙ＝Ｘβ＋ε，ε～Ｎｎ（０，σ∑）本文采用极小化均方程差的方法得到了回归系数的一种非线性有偏估计，即广义Ｓｔｅｉｎ估计，给出了它的偏差及其均方误差的渐近展开式，并且在均方误差意义下，当误差干扰充分小（σ→０）时，给出了该估计优于ＢＬＵ估计的渐近充要条件。     

完全与截尾样本时回归函数的核估计

本文得到了完全与截尾样本时回归函数核估计的强相合性．接着，构造了截尾样本的改良核估计，在Ｅ｜Ｙ｜＜∞下，得到了其强相合性．     

Admissible Linear Estimation in Linear Models

ＡｄｍｉｓｓｉｂｌｅＬｉｎｅａｒＥｓｔｉｍａｔｉｏｎｉｎＬｉｎｅａｒＭｏｄｅｌｓＬｕＣｈａｎｇｙｕ（鹿长余）ａｎｄＺｈｕＸｉａｎｈａｉ（朱显海）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｅａｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈ...     

线性变换下的模糊线性关系

在[1],[2],[3]基础上给出了某些线性变换下模糊线性无关向量组及模糊基的变换规律,指出任意模糊线性无关组都可扩充为模糊基,同时也给出了将模糊线性无关性组扩弃为模糊基的方法,。     

线性规划在回归分析中的应用

线性回归中,针对最小二乘法的两个替代准则一绝对离差和最小准则以及最大绝对离差最小准则,利用线性规划技术建立回归预测模型。实用分析表明,线性规划模型具有较好的预测效果,有郊地消除了统计数据中异常值对回归方程的影响。     

线性矩阵方程与线性矩阵方程组

研究了线性矩阵方程(组)的解的结构理论和求解方法.     

Linear Arboricity and Linear k-Arboricity of Regular Graphs

 We find upper bounds on the linear k-arboricity of d-regular graphs using a probabilistic argument. For small k these bounds are new. For large k they blend into the known upper bounds on the linear arboricity of regular graphs. Received: December 21, 1998 Final version received: July 26, 1999     

Linear Optimal Control Problems and Generalized Linear Programs

Linear optimal control problems with state inequality constraints is an important class of large systems. This paper shows that a generalized programming formulation of these problems does not result in a decomposition over time or a maximum principle as it does for problems without the state constraints. A semi-finite generalized programming formulation, however, can be used to formally produce the maximum principle, i.e. the necessary optimality conditions, for problems under consideration.     

Linear groups

The paper is based on material reviewed in RefZhMat during 1971–1977 and continues a survey of the same name which appeared in this series in 1971. In light of the Tits alternative two old areas have now acquired special importance-free linear groups and solvable linear groups; they are given special attention. Other areas are discussed in somewhat more detail than previously.Translated from Itogi Nauki i Tekhniki, Algebra, Topologiya, Geometriya, Vol. 16, pp. 35–89, 1978.     

Linear groups

This survey article covers papers abstracted inReferativnyi Zhurnal Matematika during the period 1978–1982 and is a continuation of the surveys Linear groups published in 1967, 1971, and 1977 in the seriesAlgebra, Topology, Geometry (Itogi Nauki i Tekhniki). The main things under consideration are linear groups over rings and the structure of infinite linear groups. Some very recent results are also mentioned.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 21, pp. 135–182, 1983.     

Linear ultrafilters

Let X be a k-vector space, and U a maximal proper filter of subspaces of X. Then the ring of endomorphisms of X that are “continuous” with respect to U modulo the ideal of those that are “trivial” with respect to U forms a division ring E(U). (These division rings can also be described as the endomorphism rings of the simple left End(X)-modules.) We study this and the dual construction, based on maximal cofiIters of subspaces of X, in particular, the relation between the constructed division rings and the original field or division ring k. We end by examining a more general construction in which X is a module over a general ring, given with both a filter and a cofilter of submodules.