关于拟合优度检验的EDF统计量的若干评注

拟合优度检验是建立统计模型的一个重要手段，很多检验统计量用一个理想样本能达到它们自己的极值，但ＥＤＦ统计量做不到，这无疑会影响检验的势，在本文中，我们将提出某些调整型ＥＤＦ统计量，它们具有这些性质，并改进了ＥＤＦ检验，蒙得卡罗模拟表明，调整型ＥＤＦ统计量在很多场合要必ＥＤＦ具有更高的优势，特别对重尾的备选分布更是这样，我们还考察了检验的形态与它们的极值点之间的关系。     

极值分布和威布尔分布异常数据的检验方法

本文对威布尔分布的极值分布异常数据的检验给出了一系列的方法，首先，导入了极值分布下一般Ｄｉｘｏｎ型统计量的精确分布，同时还给出了改进的Ｇ型统计量，及它们的分位点表。最后本文提出了一个新的统计量；Ｆ型统计量，并用Ｍｏｎｔｅ－Ｃａｒｌｏ模拟的方法给出其分位点表，从而首次给出威布尔分布异常值的直接检验方法。本文进一步讨论了这些检验方法的功效，且表明Ｆ型检验是最优的。     

二元极值分布的独立性检验及在沪深股市分析中的应用

提出了二元极值分布的一个独立性检验统计量 T5,导出了它的渐近分布 ,得出了模拟分位点 ,并在小样本情况下 ,与其它已有的统计量进行比较 .结果说明本文给出的统计量 T5具有与似然比检验统计量 T3几乎相同的功效 ,且比其它检验方法有效 .最后对中国沪深两市的股票收盘指数的极值进行了独立性检验 ,认为具有显著的相关性 .     

带季节线性趋势的季节时间序列的单位根检验

本文为检验带季节线性趋势的季节时间序列的单位根，提出了调整季节线性趋势的统计量，导出这些统计量的极限分布，并用Monte Carlo方法比较研究这些统计量的检验势．     

基于经验分布函数的高维正态性检验（英文）

基于经验分布函数(EDF)的Kolmogorov-Smirnov (KS),Cramer-von Mises (CM)和AndersonDarling (AD)统计量是单变量正态性检验中常用的统计量.本文通过变量降维方法,提出基于EDF的广义统计量来检验高维正态性.通过蒙特卡洛方法模拟了三种统计量的近似临界值,并基于单变量情形下统计量的近似分布公式研究了广义统计量在原假设下的近似分布.蒙特卡洛模拟说明在某些备择假设下,所提出的统计量比现有方法功效更好.最后,本章将提出的检验方法应用于实际数据验证统计量的有效性.     

异常数据检验的屏蔽效应

本文对屏蔽效应的一系列定理进行了归纳和证明，针对极值分布或威布尔分布，讨论了文献[1]中提出的六种检验统计量的屏蔽效应，文中仅给出了对Dixon型和F型统计量的结果，说明F型统计量能避免屏蔽效应。     

利用加权对称估计量对季节性时间序列的单位根检验

本文提出对季节性时间序列利用加权对称估计量的单位根检验,导出相应统计量的极限分布。用MonteCarlo方法计算经验百分位数及检验势,并对最小平方估计量,简单对称估计量和加权对称估计量的经验检验势作了比较。     

线性度量误差模型的序列相关检验

回归模型的序列相关检验是经济和金融数据分析中的一项重要的工作.基于最小二乘残差,作者提出了一个检验统计量以检验线性度量误差模型的误差序列是否存在序列相关性.在零假设下,得到了检验统计量的渐近分布.数值模拟结果表明,这里提出的检验统计量具有良好的有限样本性质.     

完全区组设计下基于Aligned秩的有方向检验问题

本文基于Aligned秩给出了用于解完全区组设计有方向检验问题的, 我们称之为$C$-检验的检验方法. 本文分别对每个试验单元仅有一个观测值以及等重复观测值和不等重复观测值各种情形下的$C$检验进行了讨论, 并在原假设$H_0$成立时计算了上述各种情形下$C$检验统计量的数学期望和方差, 且证明了$C$检验统计量的渐近分布为正态分布.     

GARCH模型参数变化的残量检验

本文研究GARCH模型参数变化的检验问题. 给出残量累积和统计量, 在原假设下得到了统计量的极限分布; 模拟结果表明残量检验可以弥补Kim, Cho和Lee (2000)\ucite{1}提出的平方累积和检验的某些不足, 比如经验势函数值过低的问题.     

一类相合的分位点型检验

广义非参数似然比检验统计量是一类很广的统计量,包含了众多重要的检验统计量,如Anderson-Darling(AD)等.利用Rubin的随机经验分布函数替代经验分布函数的方法,得到了广义非参数似然比检验统计量的新版本,构造了新的检验统计量.由于新的检验统计量在给定样本下仍然是随机变量,选择了它的分位点和期望作为检验统计量,分别称之为分位点型检验统计量和期望型检验统计量.在简单假设情况下,证明了分位点型检验统计量和期望型检验统计量在固定备择下的相合性.模拟结果显示,在某些备择下,新的检验的功效明显高于原有的基于经验分布函数的检验的功效.     

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??Kolmogorov-Smirnov (KS), Cramer-von Mises (CM) and Anderson-Darling (AD) test, which are based on empirical distribution function (EDF), are well-known statistics in testing univariate normality. In this paper, we focus on the high dimensional case and propose a family of generalized EDF based statistics to test the high-dimensional normal distribution by reducing the dimension of the variable. Not only can we approximate the corresponding critical values of three statistics by Monte Carlo method, we also can investigate the approximate distributions of proposed statistics based on approximate formulas in univariate case under null hypothesis. The Monte Carlo simulation is carried out to demonstrate that the performance of proposed statistics is more competitive than existing methods under some alternative hypotheses. Finally, the proposed tests are applied to real data to illustrate their utility.     

基于Beta分布形状的拟合优度检验

本文指出了拟合优度检验中选用经验频率公式时存在的误区,对顺序统计量失效概率分布进行了偏态和峰态分析,提出了一个基于Beta分布形状特征的经验分布函数,给出了精确值和近似值两种计算方法,在此基础上建立新的极值型检验统计量．利用Monte Carlo方法进行数值模拟,得到0．01、0．05、0．1显著度水平下检验统计量的临界值,并利用常用的分布模型进行检验功效比较,数值模拟结果表明基于分布形状的经验频率公式能更好地反映顺序统计量失效概率分布的集中趋势,证明了本文提出的两种检验统计量在中小样本条件下具有更优的检验功效．     

Multivariate nonparametric tests in a randomized complete block design

In this paper multivariate extensions of the Friedman and Page tests for the comparison of several treatments are introduced. Related unadjusted and adjusted treatment effect estimates for the multivariate response variable are also found and their properties discussed. The test statistics and estimates are analogous to the traditional univariate methods. In test constructions, the univariate ranks are replaced by multivariate spatial ranks (J. Nonparam. Statist. 5 (1995) 201). Asymptotic theory is developed to provide approximations for the limiting distributions of the test statistics and estimates. Limiting efficiencies of the tests and treatment effect estimates are found in the multivariate normal and t distribution cases. The tests are rotation invariant only, but affine invariant versions can be easily constructed. The theory is illustrated by an example.     

具有结构变化的非线性回归模型的阶段异方差检验

对于具有结构变化的非线性回归模型,两阶段的随机误差同时具有方差齐性是一个基本假设,但是该假设未必正确．本文研究该模型阶段异方差的检验问题．首先探讨了两阶段异方差的同时检验,然后构造了两阶段异方差的两个单个检验,分别得到了同时检验和单个检验的score统计量以及相应的调整形式．然后应用得到的检验统计量分析了南澳大利亚洋葱数据的阶段异方差性(Ratkowsky,1983),并用AIC,SBC进行模型比较,得到的结果与检验结果非常吻合．最后,用Monte Carlo模拟方法研究了统计量的检验功效．     

Strong Domain of Attraction of Extreme Generalized Order Statistics

It is a well-known result in extreme value theory that the von Mises conditions imply the strong convergence of extreme order statistics. We extend this result to extreme generalized order statistics. A characterization of strong domains of attraction of joint distributions of a fixed number of extreme generalized order statistics by means of the corresponding result for generalized maxima is given. In particular, we determine the asymptotic joint distribution of (upper and lower) extreme generalized order statistics. Finally, we show that the Hill estimator based on extreme generalized order statistics is asymptotic normal.     

Testing Regression Coefficients in High-Dimensional and Sparse Settings

In the high-dimensional setting, this article considers a canonical testing problem in multivariate analysis, namely testing coefficients in linear regression models. Several tests for highdimensional regression coefficients have been proposed in the recent literature. However, these tests are based on the sum of squares type statistics, that perform well under the dense alternatives and suffer from low power under the sparse alternatives. In order to attack this issue, we introduce a new test statistic which is based on the maximum type statistic and magnifies the sparse signals. The limiting null distribution of the test statistic is shown to be the extreme value distribution of type I and the power of the test is analysed. In particular, it is shown theoretically and numerically that the test is powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature.     

Detecting distributional changes in samples of independent block maxima using probability weighted moments

The analysis of seasonal or annual block maxima is of interest in fields such as hydrology, climatology or meteorology. In connection with the celebrated method of block maxima, we study several tests that can be used to assess whether the available series of maxima is identically distributed. It is assumed that block maxima are independent but not necessarily generalized extreme value distributed. The asymptotic null distributions of the test statistics are investigated and the practical computation of approximate p-values is addressed. Extensive Monte-Carlo simulations show the adequate finite-sample behavior of the studied tests for a large number of realistic data generating scenarios. Illustrations on several environmental datasets conclude the work.     

多元威布尔分布形状参数相等的似然比检验

将多元威布尔分布形状参数相等的检验转化为多元极值分布尺度参数相等的检验,利用Logistic模型的似然比统计量,给出相关参数为0．3,0．5,0．8时,检验统计量的模拟分位数和功效,指出相关参数越小,似然比统计量的功效越大。     

Testing for Spherical Symmetry of a Multivariate Distribution

We consider a test for spherical symmetry of a distribution in ^dwith an unknown center. It is a multivariate version of the tests suggested by Schuster and Barker and by Arcones and Giné. The test statistic is based on the multivariate extension of the distribution and quantile functions, recently introduced by Koltchinskii and Dudley and by Chaudhuri. We study the asymptotic behavior of the sequence of test statistics for large samples and for a fixed spherically asymmetric alternative as well as for a sequence of local alternatives converging to a spherically symmetric distribution. We also study numerically the performance of the test for moderate sample sizes and justify a symmetrized version of bootstrap approximation of the distribution of test statistics.