多项分布总体的相等对增凸序问题的多样本检验

概率分布间随机序在实践中已经得到了广泛的应用,而且似然比检验是用以检验涉及随机序问题的最普遍的检验方法．但是,关于多个多项式总体间的增凸序约束的统计推断问题并没有得到充分发展．多样本的增凸序对无约束的检验问题已被研究．然而,多总体的相等性对增凸序的假设检验问题似乎更有研究意义．并且分布的相等对随机序的假设检验问题往往是统计学家最为普遍地考虑．对多样本的情况,本文考虑了分布的相等对增凸序的假设检验问题,并且获得似然比检验统计量的零渐近分布,它是一组x~2分布随机变量的加权和,即■~2分布．     

逆Weibull分布随机变量的随机比较

研究了两个相互独立的逆Weibull分布随机变量间的随机序,似然比序,危险率序以及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系．也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系．     

逆Weibull分布随机变量的随机比较(英文)

研究了两个相互独立的逆Weibull分布随机变量间的随机序,似然比序,危险率序以及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.     

Ⅰ型极值分布随机变量的随机比较(英文)

研究了两个相互独立的Ⅰ型极大值分布随机变量间的随机序,似然比序,危险率序及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系.文中也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系.     

Ⅰ型极值分布随机变量的随机比较

研究了两个相互独立的Ⅰ型极大值分布随机变量间的随机序,似然比序,危险率序及凸序之间的相互关系,给出了两个相互独立但不同分布的随机变量满足各种随机序时其分布所含参数间的相应关系．文中也给出了两组相互独立但不同分布的随机变量极值间在一般随机序下的大小关系．     

线性模型中假设是凸锥时似然比统计量的零分布

对于有正态误差和已知协方差阵的线性模型,讨论了参数域是凸锥的假设检验问题．在考察了似然比统计量的性质后,表明了只要似然比统计量是观察值的凸函数,则似然比统计量的零分布是Ｘ２－分布的混合,而此前的结果是仅当零假设或备择假设形成线性空间时才可用．     

方差未知时两样本正态混合模型齐-性的修正似然比检验

本文讨论了方差未知时检验两样本正态混合模型齐一性的修正似然比统计量的极限性质,证明了原假设下修正似然比统计量的渐近分布为自由度为1的卡方分布.     

方差未知时两样本正态混合模型齐一性的修正似然比检验

本文讨论了方差未知时检验两样本正态混合模型齐一性的修正似然比统计量的极限性质,证明了原假设下修正似然比统计量的渐近分布为自由度为1的卡方分布.     

两个总体相等的广义似然比检验

利用广义似然比检验的原理,首先求出广义似然比统计量的极限分布,然后给出了两个总体相等的广义似然比检验方法,并且给出了随机模拟结果.     

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.     

Modified likelihood ratio test for homogeneity in normal mixtures with two samples

This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.     

不等式约束条件下经验似然法在两总体中位数检验中的应用

本文中, Owen 引入的经验似然方法被用于参数空间带不等式约束的两总体中位数的比较. 迄今为止, 还没有人研究过该问题. 这是因为, 在构造经验似然函数过程中所使用的辅助函数不是光滑函数, 因而不是凸函数, 从而使研究难度大大增加. 然而, 通过引入经验过程的办法, 本文很巧妙地解决了此问题. 根据经验过程, 本文证明了两中位数比较的经验似然比检验统计量的极限分布要么是单一的卡方分布, 要么是两个卡方分布的等权混合分布. 这一理论结果得到了模拟运算结果的有力支持.     

The effects of nonnormality on asymptotic distributions of some likelihood ratio criteria for testing covariance structures under normal assumption

This paper examines asymptotic distributions of the likelihood ratio criteria, which are proposed under normality, for several hypotheses on covariance matrices when the true distribution of a population is a certain nonnormal distribution. It is well known that asymptotic distributions of test statistics depend on the fourth moments of the true population's distribution. We study the effects of nonnormality on the asymptotic distributions of the null and nonnull distributions of likelihood ratio criteria for covariance structures.     

On Tests of Symmetry Against One-Sided Alternatives

To test that an experimental treatment is better than an existing one (or control), one can equivalently consider the difference in their response and test if the distribution of the difference is symmetric (about zero) versus it exhibits positive bias (skewness to the right). In this paper, we test the symmetry (about zero) of a discrete distribution against two particular classes of one sided alternatives. We obtain the maximum likelihood estimators under each alternative. The asymptotic null distributions of the likelihood ratio statistics are shown to have chi-bar square type distributions. A power study is performed to compare these one-sided alternatives with other one-sided tests. The theory developed is illustrated by an example.     

The block sphericity test—exact and near‐exact distributions for the likelihood ratio statistic

Using a suitable decomposition of the null hypothesis of the sphericity test for several blocks of variables, into a sequence of conditionally independent null hypotheses, we show that it is possible to obtain the expressions for the likelihood ratio test statistic, for its hth null moment, and for the characteristic function of its logarithm. The exact distribution of the logarithm of the likelihood ratio test statistic is obtained in the form of a sum of a generalized integer gamma distribution with the sum of a given number of independent logbeta distributions, taking the form of a single generalized integer gamma distribution when each set of variables has two variables. The development of near‐exact distributions arises, from the previous decomposition of the null hypothesis and from the consequent‐induced factorization of the characteristic function, as a natural and practical way to approximate the exact distribution of the test statistic. A measure based on the exact and approximating characteristic functions, which gives an upper bound on the distance between the corresponding distribution functions, is used to assess the quality of the near‐exact distributions proposed and to compare them with an asymptotic approximation on the basis of Box's method. Copyright © 2011 John Wiley & Sons, Ltd.     

分层关联表中伞形序对无约束问题的检验

概率分布间的随机序是应用概率论与统计推断中的一个重要概念. 基于交叉分类数据的趋势检验问题已被广泛地研究, 并且分层关联表广泛存在于实践中. 似然比检验方法常用于涉及随机序约束问题的检验. 对带序约束的分层关联表, 该文介绍了一种不基于模型假定的似然比检验方法, 并且给出了检验统计量的极限分布.     

Bivariate Birnbaum–Saunders distribution and associated inference

Univariate Birnbaum–Saunders distribution has been used quite effectively to model positively skewed data, especially lifetime data and crack growth data. In this paper, we introduce bivariate Birnbaum–Saunders distribution which is an absolutely continuous distribution whose marginals are univariate Birnbaum–Saunders distributions. Different properties of this bivariate Birnbaum–Saunders distribution are then discussed. This new family has five unknown parameters and it is shown that the maximum likelihood estimators can be obtained by solving two non-linear equations. We also propose simple modified moment estimators for the unknown parameters which are explicit and can therefore be used effectively as an initial guess for the computation of the maximum likelihood estimators. We then present the asymptotic distributions of the maximum likelihood estimators and use them to construct confidence intervals for the parameters. We also discuss likelihood ratio tests for some hypotheses of interest. Monte Carlo simulations are then carried out to examine the performance of the proposed estimators. Finally, a numerical data analysis is performed in order to illustrate all the methods of inference discussed here.     

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 the change of the mean-reverting parameter of an autoregressive model with stationary Gaussian noise

The likelihood ratio test for a change in the mean-reverting parameter of a first order autoregressive model with stationary Gaussian noise is considered. The test statistic converges in distribution to the Gumbel extreme value distribution under the null hypothesis of no change-point for a large class of covariance structures including long-memory processes as the fractional Gaussian noise.

     

平衡增加的经验欧氏似然

经验(欧氏)似然方法是近年来非常流行的一种非参数统计方法.针对经验(欧氏)似然的凸包限制和计算复杂问题,本文借助Emerson和Owen (2009)所提出的平衡增加思想对经验欧氏似然进行修正,得到了平衡增加的经验欧氏似然.随后论文从理论和模拟两个方面进行了研究.理论上给出了该方法与经验欧氏似然检验函数之间的联系,即在固定的样本量n下随着添加点位置的连续变化,检验方法可以从简单的均值增加经验欧氏似然变化到经验欧氏似然检验;模拟结果显示,适当选取调整因子,平衡增加的经验欧氏似然相对于(调整)经验欧氏似然而言,在大多数情况下,其分布更接近于对应的极限分布.