Chi-squared tests for general composite hypotheses from censored samples

We give chi-squared goodness-of-fit tests for parametric models including various regression models such as accelerated failure time, proportional hazards, generalized proportional hazards, frailty models, transformation models, models with cross-effects of survival functions. Choice of random grouping intervals as data functions is considered.     

k-U统计量的渐进正态性

称 为k-U统计量,其中g(x1,…,xm)是一对称函数,k为小于等于n的自然数,k可能依赖于n.这一表达形式是一类统计量,在k=n时, Unm,n就是U-统计量.本文证明了Unm,k的渐进正态性.     

VaR的统计检验

根据VaR的基本原理,对VaR的有效性进行了讨论.关于VaR提出了一个基于二点分布的检验模型,证明了存在一致最优检验,并给出了检验的表达式和拒绝域,同时鉴于金融数据的庞大性,又提出了基于渐近正态分布的检验模型,给出了检验的表达式和拒绝域.     

不等方差线性模型中的AP统计量与信息比统计量

对线性模型：Y=Xβ ρ，E（ρ）=0,cov(ρ）=σ^2G,G=diag(g1,…gn)，探讨了单个数据点对σ^2的估计-↑σ^2，β的估计-↑β的广义方差|cov-↑β|及Fisher信息阵：σ^2X′G^-1X的影响，给出了度量准则和它的化简式及统计解释。     

Estimating the Number of Clusters via the GUD Statistic

Estimating the number of clusters is one of the most difficult problems in cluster analysis. Most previous approaches require knowing the data matrix and may not work when only a Euclidean distance matrix is available. Other approaches also suffer from the curse of dimensionality and work poorly in high dimension. In this article, we develop a new statistic, called the GUD statistic, based on the idea of the Gap method, but use the determinant of the pooled within-group scatter matrix instead of the within-cluster sum of squared distances. Some theory is developed to show this statistic can work well when only the Euclidean distance matrix is known. More generally, this statistic can even work for any dissimilarity matrix that satisfies some properties. We also propose a modification for high-dimensional datasets, called the R-GUD statistic, which can give a robust estimation in high-dimensional settings. The simulation shows our method needs less information but is generally found to be more accurate and robust than other methods considered in the study, especially in many difficult settings.     

Beta Approximation to the Distribution of Kolmogorov-Smirnov Statistic

The distribution of Kolmogorov-Smirnov statistic can be globally approximated by a general beta distribution. The approximation is very simple and accurate. It can be easily implemented in any statistical software. Therefore, we can use a beta distribution to find the practical p-value of a goodness-of-fit test, which is much simpler than existing methods in the literature.     

斜球变量的F统计量

本文研究斜球变量的F统计量的性质并引进了一类斜F分布.我们得到了密度函数,分布函数,矩发生函数和矩,考察了F检验在斜正态分布族内的性质.     

A Statistic on Involutions

We define a statistic, called weight, on involutions and consider two applications in which this statistic arises. Let I(n) denote the set of all involutions on [n](={1,2,..., n}) and let F(2n) denote the set of all fixed point free involutions on [2n]. For an involution , let || denote the number of 2-cycles in . Let[ n] _q =1+q++q^n-1 and let denote the q-binomial coefficient. There is a statistic wt on I(n) such that the following results are true.(i) We have the expansion

The Search for the Ultimate Baseball Statistic

Abstract

The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century by David Salsburg. New York: W. H. Freeman and Co., 2001, pp. xi + 340, $23.95. Reviewed by Todd E. Bodner

Statisticians of the Centuries by C. C. Heyde and E. Seneta (Eds.). New York: Springer-Verlag, 2001, pp. xii + 500, $45.95. Reviewed by Todd E. Bodner     

上海证券指数的统计分析

金融市场是一个典型的复杂系统，而复杂系统在物理学中已被广泛研究。我们首次有机会获得中国大陆金融市场的上海证券指数若干年内的高频(10秒间隔)数据。本对1999年全年的上证指数进行了统计分析，发现收益率符合Levy稳定分布，而非传统经济学主张的正态分布。对上证指数的时间相关性的研究表明。上证指数的波动率在很长的时间尺度上是相关的。这将有助于在新的框架下建立新的经济学模型。     

On Continuity of the Pearson Statistic and Sample Quantiles

Convergence with probability one (in probability) of sequences of the sample quantiles and the Pearson statistic that are formed by columns of N× n arrays of random variables and bivariate random vectors respectively is established, n→ ∞. Two applications for the continuity of the Pearson statistics, when sampling is only possible along a sequence converging to an inaccessible targeting value, are presented     

生物种群的一类统计模型

以往关于生物种群增长的数学模型多是用微分方程和概率极限定理的方法来推导的。本文改用回归分析 ,系数显著性检验和残差检验的方法 ,直接从统计数字出发 ,得出美国人口在1880— 1960年的人口数字增长模型——正态前升模型。它是拟合得很好的不同以往的模型。并给出了初步的解释。     

病人满意度影响因素的统计分析

本文在文献研究的基础上,选择了可能影响病人满意的27个指标,通过因子分析,把这27个指标综合成了5个因子,即医护人员技术与能力、医护人员的态度、医疗效果、花费、医疗环境和就医(辅助)过程5个方面;论文进一步对这5个方面构成的量表的可靠性作了验证;最后,应用多元回归技术分析了5个因子对病人满意度的影响程度,为医院提高病人满意度提供了科学的依据。     

A Statistic for Testing the Null Hypothesis of Elliptical Symmetry

We present and study a procedure for testing the null hypothesis of multivariate elliptical symmetry. The procedure is based on the averages of some spherical harmonics over the projections of the scaled residual (1978, N. J. H. Small, Biometrika65, 657–658) of the d-dimensional data on the unit sphere of ^d. We find, under mild hypothesis, the limiting null distribution of the statistic presented, showing that, for an appropriate choice of the spherical harmonics included in the statistic, this distribution does not depend on the parameters that characterize the underlying elliptically symmetric law. We describe a bivariate simulation study that shows that the finite sample quantiles of our statistic converge fairly rapidly, with sample size, to the theoretical limiting quantiles and that our procedure enjoys good power against several alternatives.     

模式识别的Fuzzy统计方法及应用

运用模糊数学的概念和方法对具有模糊性的观测结果进行处理和识别 ,构成了模糊模式识别的基本内容 .利用 Fuzzy统计的方法建立了模式识别的数学模型 ,并编出模型的计算机程序 .按照科技部、教育部关于科研评价的“目标导向、分类实施、客观公正、注重实效”的要求 ,将上述程序应用于科研项目的评审中 ,克服了以往评审过程单一化、主观化的缺点 ,使评审客观、公正、合理 ,易于操作 .     

Denert's Permutation Statistic Is Indeed Euler-Mahonian

A conjecture by Marleen Denert concerning a bivariate statistic on the permutation group is proved. The statistic has the same distribution as the pair consisting of the number of descents and the major index.     

Likelihood Ratio Statistic for Exponential Mixtures

Let f ₀(x) be the exponential density and f (x) the translation model. Let (X _i) _i=1,n be i.i.d. random variables, with density g. We test that g is f ₀ against g is a simple mixture, using the LRT statistic. We prove that the LRT diverges to infinity with probability 1/2 and it is equal to 0 with probability 1/2. Therefore, the classical likelihood limiting theory does not hold.     

软件统计测试的比较和改进

针对软件统计测试中随机测试和分域测试的优劣问题，章对这两种测试方法进行了全面的比较，从理论上证明了分域测试优于随机测试。并根据软件验收的实际情况，提出了一种改进的软件测试方法，该方法有较好的测试效率。