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.     

离散型随机变量的次序统计量的分布

本文论述了离散型随机变量的次序统计量的分布律及其有关推论 .     

Approximation and Simulation of the Distributions of Scan Statistics for Poisson Processes in Higher Dimensions

Given a Poisson process in two or three dimensions, we are interested in the scan statistic, i.e. the largest number of points contained in a translate of a fixed scanning set restricted to lie inside a rectangular area. The distribution of the scan statistic is accurately approximated for rectangular scanning sets, using a technique that is also extended to higher dimensions. The accuracy of the approximation is checked through simulation. This revised version was published online in July 2006 with corrections to the Cover Date.     

遥感图像小波变换系数的统计分布

本文研究了遥感图像经张量积小波与非张量积多元小波变换后得到的小波系数的统计分布及其特性,得出了遥感图像经双正交9-7整数小波变换后的系数的每个高频子带在能量分布上近似关于原点对称,每个高上频子带都具有“非高斯”性,每层的三个高频子带分布相似,第一层的各子带的值在零点附近更为集中,所以在零点形成更陡更窄的“尖峰”的结论.     

测量误差模型参数变点的非参数检验

本讨论测量误差参数变点的检测问题,利用秩统计量,给出了模型只有一个变点的检验统计量,运用检验统计量渐近分布的性质,给出了一个计算检验淅近临界值的公式,由此我们可以较为客易计算检验的临界值。     

关于离散型随机变量次序统计量分布矩阵对称性猜想的探索

本文研究了离散型随机变量次序统计量的分布矩阵的对称性 ,获得了二个定理 .定理 1　服从等概率二点分布或等概率三点分布的离散型随机变量的次序统计量的分布矩阵是对称矩阵 .定理 2　取值有限且等概率的离散型随机变量的次序统计量的分布矩阵具有中心对称性 .     

Some test statistics based on the martingale term of the empirical distribution function

Summary It is proved that the martingale term of the empirical distribution function converges weakly to a Gaussian process inD[0, 1]. Some statistics for goodness-of-fit tests based on the martingale term of the empirical distribution function are proposed. Asymptotic distributions of these statistics under the null hypothesis are given. The approximate Bahadur efficiencies of the statistics to the Kolmogorov-Smirnov statistic and to the Cramér-von Mises statistic are also calculated. The Institute of Statistical Mathematics     

A bartlett-type adjustment for the likelihood ratio statistic with an ordered alternative

For testing the equality of normal variances with an increasing alternative, under the null hypothesis the likelihood ratio test statistic is asymptotically distributed as a mixture of chi-squared distributions. In this paper a Bartlett-type adjustment is proposed to improve the approximation of the null distribution of the likelihood ratio test statistic with an ordered alternative.     

On the Optimality of Estimators Based on P-Sufficient Statistics

For estimation of functions involving only parameters of interest, in the presence of nuisance parameters, some optimality properties are established for partially sufficient (i.e. p-sufficient) statistics in two classes of regular probability models. The results are based on a characterization of regular unbiased estimating functions for parameters of interest in probability models for which a statistic exists such that its marginal distribution depends on unknown parameters only through the parameters of interest.     

ASYMPTOTIC DISTRIBUTION OF LIKELIHOOD RATIO STATISTIC FOR TESTING SPHERICTY IN GROWTH CURVE MODELS

1IntroductionTheideaofgeneralizedgrowthcurvemodelsmeanswhereY=(yi,y2,''tAN)isapxNobservationmains;bothBandAarematrixeswithknownconstantelementsoforderpxqandmxNrespectively:(isaqxinparametermatriX;e=(el,ez,'',eN)isarandomerrorrnatrisoforderNxN;Zisanonnegativedefitiveparametermatrixoforderpxp,W=(wij)isaNxNnon-negativedefitivernatriswithknownelements.LetYdenoteamatriXwhosecoluxnnvectorsarethecorrelatedsaxnpleswithsizeNfroma"dimensionalnormalpopulation.Thecovariancematrixofthepopulationis…     

Asymptotic distribution of the LR statistic for equality of the smallest eigenvalues in high-dimensional principal component analysis

This paper deals with the distribution of the LR statistic for testing the hypothesis that the smallest eigenvalues of a covariance matrix are equal. We derive an asymptotic null distribution of the LR statistic when the dimension p and the sample size N approach infinity, while the ratio p/N converging on a finite nonzero limit c(0,1). Numerical simulations revealed that our approximation is more accurate than the classical chi-square-type approximation as p increases in value.     

On the second order local comparison between perturbed maximum likelihood estimators and Rao's statistic as test statistics

A bias-adjusted maximum likelihood estimator (mle), which has been shown to possess certain optimality criteria as an estimate of θ (see Ghosh, J. K., Sinha, B. K., and Joshi, S. N. (1982). In Statistical Decision Theory and Related Topics III (S. S. Gupta and J. O. Berger, Eds.), Vol. 1, pp. 403–456. Academic Press, Orlando, FL) is compared with Rao's statistic as a test statistic for the standard two-sided testing problem. It is shown that Rao's statistic is locally superior to any bias-adjusted mle in the sense of Chandra and Joshi (1983, Sankhy Ser. A 45 226–246). A second interpretation of a conjecture of C. R. Rao is proposed and Rao's statistic is shown to be superior as a test statistic according to the new interpretation as well. The last fact provides an interesting supplement to the results of Chandra and Joshi (1983, Sankhy Ser. A 45 226–246). Furthermore, a partial reason for the inferiority of the likelihood ratio and Wald's statistic to Rao's statistic is supplied and certain regularity assumptions of the last paper are eliminated. Finally, the local powers of certain modified versions of Rao's and Wald's statistics (see Skovgaard, I. M. (1985). Ann. Statist. 13 534–551) are studied.     

The asymptotic normality of an intermediate order statistic of the ranges of sub-samples

An intermediate order statistic based on the ranges of sub-samples is introduced and its limiting distribution derived under certain regularity conditions.This research was supported by grants from the FRD of South Africa.     

Asymptotic distribution of rank statistics under dependencies with multivariate application

By modifying the method of projection, the results of Hajek and Huskova are extended to show the asymptotic normality of signed and linear rank statistics under general alternatives for dependent random variables that can be expressed as independent vectors of fixed equal length. The score function is twice differentiable; the regression constants are arbitrary; and the distribution functions are continuous, but arbitrary. As an application, a rank transform statistic is proposed for the one-sample multivariate location model. The ranks of the absolute values of the observations are calculated without regard to component membership, and the scored ranks are substituted in place of the observed values. The limiting distribution of the proposed test statistic is shown to be χ² divided by the degrees of freedom under the null hypothesis, and noncentral χ² divided by the degrees of freedom under the sequence of Pitman alternatives.     

股票市场渐进效率的实证分析

深发展(A0001)自1993 4 9至2001 4 9的日收盘价的统计分布呈"双峰分布":早期(93 4 9～96 5 31)表现出左偏态分布,近期(96 6 3～2001 4 9)呈近似正态分布,这说明我国股市尚未达到半强有效;但是,本文还分析了两个阶段A0001的日、周、半月、月、季、半年和年收益率分布,发现二者随着"时间之窗"的增长而渐进有效。     

误差服从多元t分布的一类线性模型下参数估计的若干注记

研究一类线性模型下参数估计的若干问题．这类模型包含了多个因变量线性模型、增长曲线模型、扩充的增长曲线模型、似乎不相关回归方程组、方差分量模型等常用模型．在这类线性模型下,证明了当误差服从多元t分布时与误差服从多元正态分布时,具有相同的完全统计量和无偏估计,且在后一种情况下的充分统计量必为前一种情况下的充分统计量．对于带有多种协方差结构的前述几种模型,把在误差服从多元正态分布下,相应的协方差阵及有关参数的一致最小风险无偏(UMRU)估计存在性的结论推广到了相应的误差服从多元t分布情形．此外,对于误差服从多元t分布的这类统一的线性模型,给出了回归系数的线性可估函数的无偏估计的协方差阵的C-R下界．     

A semiparametric Wald statistic for testing logistic regression models based on case-control data

We propose a semiparametric Wald statistic to test the validity of logistic regression models based on case-control data. The test statistic is constructed using a semiparametric ROC curve estimator and a nonparametric ROC curve estimator. The statistic has an asymptotic chisquared distribution and is an alternative to the Kolmogorov-Smirnov-type statistic proposed by Qin and Zhang in 1997, the chi-squared-type statistic proposed by Zhang in 1999 and the information matrix test statistic proposed by Zhang in 2001. The statistic is easy to compute in the sense that it requires none of the following methods: using a bootstrap method to find its critical values, partitioning the sample data or inverting a high-dimensional matrix. We present some results on simulation and on analysis of two real examples. Moreover, we discuss how to extend our statistic to a family of statistics and how to construct its Kolmogorov-Smirnov counterpart. This work was supported by the 11.5 Natural Scientific Plan (Grant No. 2006BAD09A04) and Nanjing University Start Fund (Grant No. 020822410110)     

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.     

贫困测度动态研究

把贫困测度作为样本的函数,即是一个统计量,进而探讨其均值和方差,以及在某一区间的概率.利用中国营养与健康调查8个年度的数据,计算贫困测度的均值.和传统的贫困测度相比,贫困测度作为统计量更多地综合了样本的信息,将静态的贫困测度转化为动态的统计量,为我国扶贫工作提供决策依据更具有理论价值和现实意义.     

修正贝叶斯控制图与累积和控制图的比较分析

面向多品种、小批量制造过程的小波动检验是目前统计过程控制图发展和研究的方向.在对修正贝叶斯控制图与累积和控制图原理进行比较后,通过一组过程仿真数据对两种控制图进行了分析,指出了两种控制图的特性和应用前景.