On two asymptotic normal distributions for the generalized wilks lambda statistic

In this paper we.present a Normal asymptotic distribution for the logarithm of the generalized Wilks Lambda statistic based on an asymptotic distribution for the determinant of a Wishart matrix. This distribution is obtained through the combined use of Taylor expansions of random variables whose exponentials have chi-square distributions and the Lindeberg-Feller version of the Central Limit Theorem, Another asymptotic Normal distribution for the logarithm of the generalized Wilks Lambda statistic for the case when at most one of the sets has an odd number of variables is derived directly from the exact distribution. Both distributions are non-degenerate and non-singular. The first Normal distribution compares favorably with other known approximations and asymptotic distributions namely for large numbers of variables and small sample sizes, while the second Normal distribution, which has a more restricted application, compares in most cases highly favorably with other known asymptotic distributions and approximations. Finally, a method to compute approximate quantiles which lay very close and converge steadily to the exact ones is presented.     

对Hurwitz定理的一个推广

本文对判别实二次型正定性的重要方法之一———Hurwitz定理做了推广 ,使得本来需从实二次型的矩阵A =(aij) n×n(A′ =A)的左上角元a11开始取从 1到n阶顺序主子式进行的判定 ,变成可以从A的主对角线上任意元aii(i =1,2 ,… ,n)开始取从 1到n阶连序主子式进行判定。因此 ,本文给出的方法使用起来更为方便、灵活 ,具有一定的实用价值     

矩阵指数行列式的计算

对矩阵指数的行列式的计算问题 ,进行了理论探讨     

论社会主义政治文明的规定性

社会主义政治文明具有三重规定性政治文明规定性、社会主义规定性和国别规定性.坚持党的领导、人民当家作主和依法治国是这三重规定性的客观要求.社会主义政治文明三重规定性的有机统一决定了必须坚持党的领导、人民当家作主和依法治国的有机统一.     

AN ADAPTIVE TRIMMED LIKELIHOOD ALGORITHM FOR IDENTIFICATION OF MULTIVARIATE OUTLIERS

This article describes an algorithm for the identification of outliers in multivariate data based on the asymptotic theory for location estimation as described typically for the trimmed likelihood estimator and in particular for the minimum covariance determinant estimator. The strategy is to choose a subset of the data which minimizes an appropriate measure of the asymptotic variance of the multivariate location estimator. Observations not belonging to this subset are considered potential outliers which should be trimmed. For α less than about 0.5, the correct trimming proportion is taken to be that α > 0 for which the minimum of any minima of this measure of the asymptotic variance occurs. If no minima occur for an α > 0 then the data set will be considered outlier free.     

LAPLACE定理引理证明的一点改动

高教版《高等代数》第二章第八节中谈到行列式的乘法规则—LAPLACE定理,对该定理的证明及运用取决于对定理引理的证明。笔者在教学过程中发现,对教材中引理证明的最后几步作些改动,可使初学《高等代数》的学生更易于接受、理解。     

实阵和有理阵的一些快算复杂性

给出在Ｓｔｒａｓｓｅｎ矩阵乘法基础上的不同于文献［１］所提出的方法，但同样是的实阵行列式求值的快速算法，有理阵行列式求值的Ｏ（ｎ￣２）的快速算法和有理三角阵求逆的Ｏ（ｎ￣２）的快速算法等。     

A useful approximation for planning block designs with potential missing data

Many empirical studies are planned with the prior knowledge that some of the data may be missed. This knowledge is seldom explicitly incorporated into the experiment design process for lack of a candid methodology. This paper proposes an index related to the expected determinant of the information matrix as a criterion for planning block designs. Due to the intractable nature of the expected determinantal criterion an analytic expression is presented only for a simple 2x2 layout. A first order Taylor series approximation function is suggested for larger layouts. Ranges over which this approximation is adequate are shown via Monte Carlo simulations. The robustness of information in the block design relative to the completely randomized design with missing data is discussed.     

对数学教学语言的探讨

教师的教学语言水平 ,是课堂教学能否取得高效率的主要因素之一。教学语言是教师在教学过程中必须具备的语言工具 ,根据笔者近几年来的教学实践 ,针对数学教学方面进行了一些尝试性的摸索和总结 ,对如何使用数学教学语言进行了一些探讨     

对“关于谢邦杰的一个定理推广”一文的注记

得到了如果四元数体上的矩阵Ａ＝（ａ（ｉｊ））ｍ×ｎ的行向量都不是零向量，那么有　，这一结果改进或推广了已有文献的结论。