假设检验中的原假设选取问题

针对假设检验中"对一个具体问题,在相同的显著性水平α下进行假设检验,如果交换原假设和备择假设,得到的结论可能完全相反"这一问题进行分析,并给出根据实际问题的要求如何正确建立原假设和备择假设的方法.     

一类单边假设检验问题原假设和备择假设的判别分析

在单边假设检验问题中,原假设和备择假设的地位一般是不对等的,将两者互换就有可能得到矛盾推断.文章既给出了现有的解析方法,也从描述性统计和推断性统计相结合,以及控制第Ⅱ类错误发生概率的角度给出了进一步的思考,合理解析了单边假设检验出现矛盾推断的难题.     

多元分布下单边备择假设的两步检验

x~2检验是熟知的拟合优度检验.它适用于任意的备择假设,尤其是适用于一般的备择假设"H_0不真"的情况.但是,当备择假设是一个单边假设时,x~2检验没有用到单边假设所提供的信息.因此,一个充分利用单边备择假设信息的检验是有可能优于传统的x~2检验的.本文就是利用单边备择假设的信息给出了一个两步检验,并通过一个例子,详细介绍了两步检验法的实施,说明了其应用.     

关于假设检验中原假设的提出

在假设检验中第一步要解决的,也是最为困难的问题就是原假设H0的提出.本文对假设检验的原理给出了解释,并通过一个实例的讨论给出了原假设H0提出的原则.     

模糊Bayes检验

本文对原假设和备择假设中参数是模糊子集的假设检验问题，引入了模糊Ｂａｙｅｓ检验的概念，对简单模糊假设，给出了求模糊Ｂａｙｅｓ检验的方法，讨论了它的性质，并针对一类特殊的隶属函数，得出了检验的具体公式。最后，通过几个数值实例，表明了模糊Ｂａｙｅｓ检验的优良性。     

改进的基于图方法对真实原假设比例的估计

在多重假设检验中,对原假设为真的比例或数量的估计是一个基础性问题.一类估计方法是基于排序p值的图方法,由Schweder和■(1982)首次提出.但是这类方法只利用了特定切点p值的信息,当原假设和备择假设差异较小时,现有方法的有效性会降低.文章通过利用所有原假设p值的信息,对估计进行了改进.由于利用了更多的信息,改进后的估计更有效.数值模拟结果表明,文章所提出的估计方法比现有方法有效性更好,最后将所提出的方法应用到实际数据分析中.     

假设检验中的三个问题及其思考

讨论了假设检验的教学和实践中可能会遇到的三个问题.分析得到三个结论:理论上原假设与备择假设可以任意设定,但实践中常常按照某种规则来设定;假设检验的两个常用的决策准则中,p值准则更精确,为决策者接受原假设提供了一个"风险"的度量;假设检验理论在处理利用样本推断总体的问题中是普遍有效的.     

论假设检验中的两类错误

蔡越江．论假设检验中的两类错误．本文从假设检验的两个例子谈起,指出备择假设也是影响接区域的。接着论述了假设检验中的两类错误之间的关系。最后讨论如何同时控制两类错误。     

确定假设检验拒绝域的证据原理

基于假设检验的证伪逻辑,阐述了确定拒绝域的证据原理.假设检验的核心思想是考察样本提供的信息与原假设之间的不一致性,也即考察样本对备择假设成立是否提供有力证据.基于小概率原理的显著性水平只是证据不符程度的一个阈值而已,强调"反证法"的思想有可能会误入歧途.     

重尾序列均值变点的经验似然比检验

本文通过经验似然思想建立假设检验的方法,研究了重尾序列均值变点的检测问题.首先,基于重尾模型,在原假设和备择假设下得到经验似然函数.其次,基于经验似然函数构造似然比检验统计量,并给出在原假设成立时该似然比统计量的渐近分布.最后,进行Monte Carlo数值模拟验证该方法的有效性,模拟结果表明本方法对重尾序列均值变点的...     

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.     

Permutation Test在假设检验中的应用

本文介绍了一种实用的、基于大量计算的统计推断方法———Permutation test。该法根据所研究的问题构造检验统计量,并利用手头样本,按排列组合的原理导出检验统计量的理论抽样分布;若难以导出确切的理论分布,则采用抽样模拟的方法估计其近似分布,然后求出从该分布中获得手头样本及更极端样本的概率(P值),并界定此概率值,作出推论。本方法属分布自由检验,适用于总体分布未知的小样本资料,以及某些难以用常规方法分析的资料之假设检验问题。本文就“Permutation”的含义,“Permutation tes”t的特点,“统计量的构造”,“模拟次数的选择”,应用进展等问题展开探讨。     

一种改进的单位根检验程序

原假设的合理设定是单位根检验的首要问题,至今尚无学者对此进行深入研究。通过剖析以往单位根检验原假设设定存在的缺陷,在同时考虑原假设的可信度和检验可靠性的前提下,本文提出了单位根检验原假设的一种合理的设定策略及改进的检验程序。     

A simple test of exponentiality against NWBUE family of life distributions

In this paper we propose a simple procedure to test the null hypothesis of exponentiality against the alternative that it belongs to the new worse then better than used in expectation (NWBUE) family. The test is shown to be consistent and the asymptotic distribution of the test statistic has been obtained. The performance of the test against various classes of alternatives has been studied by means of simulation. Copyright © 2005 John Wiley & Sons, Ltd.     

Hypothesis of multisample sphericity

The hypothesis of multisample sphericity appears in different areas such as repeated measurement designs, checking the validity of F ratios in the analysis of variance problems, and testing circularity. This article deals with the modified likelihood ratio test for testing multisample sphericity, null and nonnull moments, as well as the null and nonnull distributions of the test statistic. Some approximations are also considered.Published in Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 136, pp. 153–161, 1984.     

The new test criterion for the homogeneity of parameters of several populations

Summary The new test criterion for testing the homogeneity of parameters of several populations is proposed and the test properties of it is discussed. The asymptotic expansions of the distributions of test criterion are discussed under (i) null hypothesis, (ii) fixed alternative hypothesis and (iii) local alternative hypothesis converging to the null hypothesis with appropriate rate of convergence as the sample size increases. As a particular case the asymptotic theory of a statistic for a homogeneity of variances of normal populations is also discussed and the exact moments of it under a null hypothesis can be used to obtain a percentage point by a Pearsonian curve fitting. This Institute of statistical Mathematics     

A Semiparametric Two-Sample Hypothesis Testing Problem for Random Graphs

Two-sample hypothesis testing for random graphs arises naturally in neuroscience, social networks, and machine learning. In this article, we consider a semiparametric problem of two-sample hypothesis testing for a class of latent position random graphs. We formulate a notion of consistency in this context and propose a valid test for the hypothesis that two finite-dimensional random dot product graphs on a common vertex set have the same generating latent positions or have generating latent positions that are scaled or diagonal transformations of one another. Our test statistic is a function of a spectral decomposition of the adjacency matrix for each graph and our test procedure is consistent across a broad range of alternatives. We apply our test procedure to real biological data: in a test-retest dataset of neural connectome graphs, we are able to distinguish between scans from different subjects; and in the C. elegans connectome, we are able to distinguish between chemical and electrical networks. The latter example is a concrete demonstration that our test can have power even for small-sample sizes. We conclude by discussing the relationship between our test procedure and generalized likelihood ratio tests. Supplementary materials for this article are available online.