Nearly optimal covariate designs—Part I

We propose to discuss at length several examples from standard text books. All of these examples deal with analysis of covariance (ANCOVA) models and related analyses of data. We intend to capitalize on our understanding of optimal covariate designs (OCDs) in different ANCOVA models and re-visit these examples with a view to suggest optimal/nearly optimal designs for estimation of the covariate parameter(s). As we will see, for some examples our task is very much routine but for others, it is indeed a highly non trivial exercise.

?We intent to cover a total of six examples—divided in two parts. This is Part I—dealing with two examples.     

可对称化矩阵特征值的任意扰动

针对可对称化矩阵,研究了可对称化矩阵特征值的任意扰动和实任意扰动。从Schur分解入手,利用矩阵可对角化的性质,通过矩阵等式的恒等变形,得到了可对角化矩阵关于F-范数和Q-范数的任意扰动界。     

一些特殊的n阶方阵的基本性质

初步研究了次转置矩阵、次对称矩阵和次单位矩阵的基本性质.     

Portfolio optimization: New capabilities and future methods

Summary  This paper addresses the problem of portfolio selection in finance. In many cases, currently available software to compute the efficient frontier runs into difficulty in problems with more than about 600 securities. To proceed beyond this size, it is often necessary to modify the problem in which case there is typically a loss of information. In this paper, we discuss a computer capability that can exactly compute mean-variance efficient frontiers of problems with up to 2,000 securities in very reasonable time (even if a problem’s covariance matrix is 100% dense). The paper also discusses an augmentation to the theory of portfolio selection that allows multiple objectives (such as dividends, liquidity, social responsibility, amount invested in R&D, and so forth) to be incorporated into the portfolio selection process. In such problems, the efficient set is no longer a “frontier,” but is now best described as a “surface” with the interesting property that it is composed of platelets (like on the back of a turtle). Moreover, the computer capability that can compute the exact efficient frontier of a mean-variance problem with up to 2,000 securities also has, after additional coding, the ability to compute exactly all platelets of the efficient surface of a tri-criterion portfolio problem with up to 400 securities.

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Zusammenfassung  In dieser Arbeit stellen wir einen leistungsf?higen Rechenalgorithmus vor, um den effizienten Rand (die nichtdominierten Alternativen) von Portfolio-Auswahlproblemen in der Finanzierung zu bestimmen. Wir bezeichnen den Berechnungsalgorithmus, der in Java programmiert ist, mit MPQ (multi-parametric quadratic programming). MPQ weist gegenüber bisherigen Berechnungsverfahren eine Reihe von Vorteilen auf: Es kann für umfangreiche Anwendungsf?lle genutzt werden, ist durch passable Rechenzeiten charakterisiert und kann die Menge effizienter Alternativen in einem Bruchteil bisher üblicher Rechenzeiten bestimmen.

     

Clustering of correlation matrices: A step-wise procedure

An alternative to the criteria proposed by King [9] for clustering correlation matrices is explored. Several simple examples examined by total enumeration employing our criterion indicate that the criterion yields clusters with high within group correlation. A step-wise routine is suggested for problems of realistic size and is applied to the examples presented in King's article. Additional evidence in the form of several Monte Carlo experiments indicates that the routine performs satisfactorily in determining the optimal separation of variables into two groups.     

Weight matrices for social influence analysis: An investigation of measurement errors and their effect on model identification and estimation quality

Weight matrices, such as used in network autocorrelation models, are useful to investigate social influence processes. The objective of this paper is to investigate a key topic that has received relatively little attention in previous research, namely the issues that arise when observational limitations lead to measurement errors in these weight matrices. Measurement errors are investigated from two perspectives: when relevant ties are omitted, and when irrelevant ties are erroneously included as part of the matrix. The paper first shows analytically that these two situations result in biased estimates. Next, a simulation experiment provides evidence of the effect of erroneously coding the weight matrix on model performance and the ability of a network autocorrelation test to identify social influence effects. The results suggest that depending on the level of autocorrelation and the topology attributes of the underlying matrix, there is a window of opportunity to identify and model social influence processes even in situations where the ties in a matrix cannot be accurately observed.     

（0，1）—矩阵类U（R，S）的势函数

讨论了（０，１）—矩阵类Ｕ（Ｒ，Ｓ）中所含指定的行和向量Ｒ＝（ｒ１，ｒ２，…，ｒｍ），列和向量Ｓ＝（ｓ１，ｓ２；，…，ｓｎ）的（０，１）—矩阵的势ｆｍ，ｎ（Ｒ，Ｓ），给出了求ｆｍ，ｎ（Ｒ，Ｓ）的递归公式．     

有限域Fq上矩阵的广义逆及矩阵Kronecker积

给出了Fq上矩阵群逆和E-P逆和E-P逆及矩阵Kronecker积的弱广义Schur补定义,并讨论了其相应的特殊性质.     

On best affine prediction

The theory of best affine prediction (BAP) is extended to the vector case with possibly singular variance matrix of the predictor variable. The theory is then applied to derive Thomson’s classical predictor for factor scores, allowing for a singular variance matrix of the factors. The results are formulated in a free distribution setting. Further, Bartlett’s estimator is considered and compared with Thomson’s predictor. The authors are thankful to the two referees, one for a suggestion that led to the Addendum of the paper, and the other one for several very useful remarks. Research supported by the Spanish grant BEC2000-0983.     

秦皇岛市工业主导产业的选择

本文以秦皇岛工业现状分析为依据,采用波士顿矩阵分析法筛选出秦皇岛市具有竞争优势的产业,然后运用西方主导产业理论,构建“需求收入弹性、生产率上升率、影响力系数、感应度系数、产业链长度、产业贡献率、区位熵”等八个指标组成的区域主导产业选择基准,利用AHP法对主要产业部门进行综合评分,最后确定了金属压延业、农副食品加工业和机械工业为秦皇岛市未来的工业主导产业。