用递归关系计算n阶行列式的规律

给出了用递归关系方法求任意ｎ阶行列式的值的一般方法：首先，把已知的ｎ阶行列式看作为阶数ｎ的一个函数，记为Ｄ（ｎ）；其次，按行或按列展开这个行列式，并仔细观察存在于余子式及Ｄ（ｎ）里的关系，建立关于Ｄ（ｎ）的某一递归关系，此关系总为一个齐次的或非齐次的递归关系；最后。借助于Ｄ（０）、Ｄ（１）和Ｄ（２）等求出递归关系的通解的系数．虽然此法不一定简单，但毕竟是一个有用的方法．     

On the numerical behaviour of ARMA(P,Q) covariance determinants for various sample sizes

An algorithm for the covariance determinant of a stationary autoregressive-moving average model is considered. Some asymptotic properties of this determinant in the stationarity and invertibil-ity region of the process are studied numerically in simple special cases.     

Sensitivity Coefficient in Principal Component Analysis: Robust Case

In the classical principal component analysis (PCA), the empirical influence function for the sensitivity coefficient ρ is used to detect influential observations on the subspace spanned by the dominants principal components. In this article, we derive the influence function of ρ in the case where the reweighted minimum covariance determinant (MCD¹) is used as estimator of multivariate location and scatter. Our aim is to confirm the reliability in terms of robustness of the MCD¹ via the approach based on the influence function of the sensitivity coefficient.     

Wild adaptive trimming for robust estimation and cluster analysis

Trimming principles play an important role in robust statistics. However, their use for clustering typically requires some preliminary information about the contamination rate and the number of groups. We suggest a fresh approach to trimming that does not rely on this knowledge and that proves to be particularly suited for solving problems in robust cluster analysis. Our approach replaces the original K‐population (robust) estimation problem with K distinct one‐population steps, which take advantage of the good breakdown properties of trimmed estimators when the trimming level exceeds the usual bound of 0.5. In this setting, we prove that exact affine equivariance is lost on one hand but, on the other hand, an arbitrarily high breakdown point can be achieved by “anchoring” the robust estimator. We also support the use of adaptive trimming schemes, in order to infer the contamination rate from the data. A further bonus of our methodology is its ability to provide a reliable choice of the usually unknown number of groups.     

Controlling the size of multivariate outlier tests with the MCD estimator of scatter

Multivariate outlier detection requires computation of robust distances to be compared with appropriate cut-off points. In this paper we propose a new calibration method for obtaining reliable cut-off points of distances derived from the MCD estimator of scatter. These cut-off points are based on a more accurate estimate of the extreme tail of the distribution of robust distances. We show that our procedure gives reliable tests of outlyingness in almost all situations of practical interest, provided that the sample size is not much smaller than 50. Therefore, it is a considerable improvement over all the available MCD procedures, which are unable to provide good control over the size of multiple outlier tests for the data structures considered in this paper.     

资本结构理论与实证研究评述及设想

自Modigliani和Miller提出MM理论以来,资本结构问题一直是理论界和实务界关注的焦点。本文在对资本结构理论研究、资本结构影响因素实证研究及资本结构与企业价值实证研究进行综述的基础上,分析现有资本结构理论与实证研究存在的不足,提出进行区域资本结构研究的设想。     

母子公司营销协同影响因素的实证研究

母子公司营销协同可以使各成员在营销活动上协调一致,组成统一的整体,共享资源与能力,以实现集团整体价值的最大化。实证研究表明,母子公司营销协同的影响因素可分为协同氛围、市场统一、战略相关和管控强度等四个方面,母子公司营销协同可由有形营销协同和无形营销协同两个维度来衡量;母子公司内部协同氛围越浓厚,母子公司间、子公司间在市场和战略方面越相似,越有助于实现营销协同;协同氛围和市场统一分别是影响无形与有形营销协同实现的关键因素。     

Optimal fractional factorial designs for estimating interactions of one factor with all others: 3m Series

In some experimental situations, only one factor is expected to interact with other factors. Designs which permit estimation of all main effects and the interactions of one factor ‘With All Others’, are termed WAO designs. This paper discusses the existence and construction of s^m WAO designs. A series of WAO designs are presented for the 3^m factorial, for m = 6, 7, ... , 14. The p non-negligible effects are estimable in 9f^? runs, where f^? is the smallest integer such that 9f^? ≥p. These designs are determinant optimal within the class of parallel flats fractions and, except for the case f^? = 9, are new. They are ideally suited for sequential experiments.     

The maximization of determinants of block Toeplitz matrices with applications in optimal design theory

We consider the maximization of the determinant of the trigonometric moment matrix of a matrix measure on the unit circle. The results are analog to those obtained by Dette and Studden (2005) for moment matrices of matrix measures on a compact interval. A statistical application in optimal design theory is considered and we present several optimal designs for Fourier regression models.     

合并新村脆弱性决定因子识别——基于宁夏永宁县试验区的探索

村庄合并是对传统村镇空间结构与组织形态的重大变革,是村民生计方式与社会结构的重大调整。合并新村建设初期因为居住环境、公用基础设施、公共服务体系不够完善,常表现出一定程度的脆弱性。脆弱性扰动、敏感性、适应力是抽象概念,不可直接观测。通过构建合并新村脆弱性结构方程模型对潜在变量对应的15个观测变量进行估计,有效排除了主观性判断影响,识别出5个重要影响因子。低保水平、政民互动因子是扰动的重要影响因子,养老保险、政策兑现因子是敏感性的重要影响因子,对外交通是适应力的重要影响因子。灰色定权聚类模型克服了结构方程模型能识别重要与次要因子但无法判断影响状态的不足之处。对上述重要影响因子与县域人均GDP指标进行再评估,最终识别出4个脆弱性决定因子,其中低保水平是脆弱性的扰动决定因子,养老保险、政策兑现是脆弱性的敏感性决定因子,县域人均GDP值是脆弱性的适应力决定因子。