The exact noncentral distribution of the generalized multiple correlation matrix

Given p×n X N(βY, ∑?I), β, ∑ unknown, the noncentral multivariate beta density of the matrix L = [(YY′)^-1/2Y X′ (XX′)^-1XY′ (YY′)^-1/2] is desired. Khatri (1964) finds this density when β is of rank unity. The present paper derives the noncentral density of L and the density of the roots matrix of L for full rank β. The dual case density of L is also obtained. The derivations are based on generalized Sverdrup's lemma, Kabe (1965), and the relationship between primal and dual density of L is explicitly established.     

Order statistics from trivariate normal and -distributions in terms of generalized skew-normal and skew- distributions

We consider here a generalization of the skew-normal distribution, GSN(λ₁,λ₂,ρ), defined through a standard bivariate normal distribution with correlation ρ, which is a special case of the unified multivariate skew-normal distribution studied recently by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574]. We then present some simple and useful properties of this distribution and also derive its moment generating function in an explicit form. Next, we show that distributions of order statistics from the trivariate normal distribution are mixtures of these generalized skew-normal distributions; thence, using the established properties of the generalized skew-normal distribution, we derive the moment generating functions of order statistics, and also present expressions for means and variances of these order statistics.Next, we introduce a generalized skew-t_ν distribution, which is a special case of the unified multivariate skew-elliptical distribution presented by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574] and is in fact a three-parameter generalization of Azzalini and Capitanio's [2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. Roy. Statist. Soc. Ser. B 65, 367–389] univariate skew-t_ν form. We then use the relationship between the generalized skew-normal and skew-t_ν distributions to discuss some properties of generalized skew-t_ν as well as distributions of order statistics from bivariate and trivariate t_ν distributions. We show that these distributions of order statistics are indeed mixtures of generalized skew-t_ν distributions, and then use this property to derive explicit expressions for means and variances of these order statistics.     

Approximating the risk score for disease diagnosis using MARS

In disease screening and diagnosis, often multiple markers are measured and combined to improve the accuracy of diagnosis. McIntosh and Pepe [Combining several screening tests: optimality of the risk score, Biometrics 58 (2002), pp. 657–664] showed that the risk score, defined as the probability of disease conditional on multiple markers, is the optimal function for classification based on the Neyman–Pearson lemma. They proposed a two-step procedure to approximate the risk score. However, the resulting receiver operating characteristic (ROC) curve is only defined in a subrange (L, h) of false-positive rates in (0,1) and the determination of the lower limit L needs extra prior information. In practice, most diagnostic tests are not perfect, and it is usually rare that a single marker is uniformly better than the other tests. Using simulation, I show that multivariate adaptive regression spline is a useful tool to approximate the risk score when combining multiple markers, especially when ROC curves from multiple tests cross. The resulting ROC is defined in the whole range of (0,1) and is easy to implement and has intuitive interpretation. The sample code of the application is shown in the appendix.     

On optimal testing for the equality of equicorrelation: An example of loss in power

Sen Gupta (1988) considered a locally most powerful (LMP) test for testing nonzero values of the equicorrelation coefficient of a standard symmetric multivariate normal distribution. This paper constructs analogous tests for the symmetric multivariate normal distribution. It shows that the new test is uniformly most powerful invariant even in the presence of a nuisance parameter, σ². Further applications of LMP invariant tests to several equicorrelated populations have been considered and an extension to panel data modeling has been suggested.     

揭橥理论视域：“国进民退”争论背后的意识形态迷思

“国进民退”争议热潮背后隐藏的是以前困扰着部分中国共产党人,至今仍然困扰着部分共产党人的意识形态认知误区,回顾中国共产党宏观经济政策史和经济思想史的变迁历程,深入剖析中国共产党在意识形态层面上对“公有”和“非公有”经济成分的内在二元冲突,可以见出中国共产党要以“执政党”的自身定位来重构“革命党”时期的意识形态。     

多元视阈下的文化解读——东西《原始坑洞》析解

东西《原始坑洞》摆脱了既定的美学范式和语言秩序,虽然篇幅不长但却于短小中见张力,简赅处寓精辟,呈现出多元化的解读张力,他的文字以冷静而残酷的叙事策略完美地再现了俄狄浦斯情结的神髓、解构了“家国同构”的文化权威与禁忌、在自我放逐与命运抉择的面前选择了人性之善,并在极具反讽的文字中以不动声色的笔触表现出生命消逝与生命延续的历史命题。     

二元对立的解构与殖民主义的没落--论《耻》的后殖民主义主题

库切的代表作<耻>抓住了这一文艺思潮,以平实的语言展现了后种族隔离时代白人社会的日益没落.围绕男主人公的生活遭遇,以性别、性权、性格这几个因素为线索分析几组人物二元对立关系的形成与瓦解,运用解构主义的文学写作和批评方法揭示了原作蕴涵的殖民主义日益没落的后殖民主义主题.它对于欧洲中心论的批判具有重要意义.     

从制度伦理的视角窥探我国"三农"问题

“三农”问题是困扰我国农村建设的核心问题。“三农”问题根源于我国的二元社会经济结构中背离了正义原则的制度缺陷。科学的制度安排是“三农”问题得以解决的基本前提。从制度伦理的视角对我国的“三农”问题进行科学的审视是一种必然。要彻底解决“三农”问题,废除城乡差别,给农民以国民待遇,必须从制度创新入手。     

二元对立的矛盾纠缠——论周作人20世纪二三十年代的散文艺术

20世纪二三十年代周作人的小品文由前期浮躁凌厉之巅向平和冲淡之谷转变,追求一种闲适蕴藉、"自我表现"的趣味之风;但透过其柔和的笔调,却又可以发现其散文貌似平淡实质蕴含"苦"和"涩"之味。由此,构成了其小品散文存在平淡与苦涩矛盾对立纠缠的二元风格。具体言之,"平和冲淡"不是周作人散文的唯一风貌,"凌厉苦涩"也不是周作人散文的仅有格调。周作人的散文风格是既"平和冲淡"又"凌厉苦涩"的,是由辐射性与内敛性这二元相结合的统一体,你中有我,我中有你,既对立又纠缠。周作人小品散文纠缠于二元之间的复杂风格,既让我们看到了其散文丰富多彩的一面,也有利于我们进一步了解其颇受争议的一生。     

浅谈卡尔&#183;马克思哲学的超越本性

卡尔.马克思哲学超越了近现代种种“二元对立”的“主义”,这是其特殊的哲学本性。当今人类进入了一个和平发展的新时代,全球利益压倒了阶级、民族、国家和地区的利益,由此产生出当今最有价值的“国际化精神”和“全球意识”,这正是马克思的“国际人本主义”哲学理想超时代的展现,也是马克思哲学超越本性的当代显示。