关于区间估计与假设检验的最优性

本首先提出了区间估计的另一个优良性因素－虚假度，进而建立或疏理了区间估计与假设检验的优良性、最优性概念，然后给出了区间估计与假设检验最优性的关系。     

广义区间估计及其最优性(Ⅳ)

本文在提出了广义区间估计以及其上的最优性概念之后 ,证明了广义区间估计与假设检验的最优性之间的关系 ,推演了一个重要区间估计的最优性     

小样本下相关系数的检验与区间估计——基于Bootstrap的研究

本文首先介绍了样本相关系数的计算公式以及在联合正态分布下的假设检验和区间估计方法,同时指出了其对样本的要求,然后就小样本下相关系数的区间估计和假设检验问题给出了基于bootstrap方法的解决途径,分析表明bootstrap方法非常适合用于未知总体分布形态小样本下的区间估计与假设检验。     

两均匀分布总体参数之比的估计

给出了两均匀分布的最大次序统计量的密度函数,并讨论了两均匀分布参数之比的通常区间估计、最短区间估计及假设检验方法.最后,根据实例求出了这两种区间估计及其区间长度,并得出了相应的结论.     

不平衡两因素套设计模型中方差分量比的区间估计

给出了次样本容量相等时,不平衡两因素套设计模型中方差分量之比的广义区间估计.为了研究所得区间估计的优良性,并与Burdick,Birch and Graybill给出的修正大样本(MLS)方法进行对比,进行了模拟研究和分析.结果表明所得方法优于MLS方法,特别是在极端不平衡情形.     

小样本的均匀分布参数的区间估计和假设检验

本文提出了小样本的均匀分布参数的区间估计和假设检验方法 .数值模拟计算后效果良好     

艾拉姆咖分布参数的Bayes估计及检验

首先给出了艾拉姆咖分布在定数截尾场合下参数的极大似然估计;其次由"平均剩余寿命"的概念得到了参数的拟矩估计;然后取共轭先验分布给出了参数的经验Bayes估计、区间估计及假设检验;最后通过实例给出了不同截尾样本下参数的点估计和区间估计.     

至多一个变点模型的统计推断

对至多一个变点模型,其中‘(1/n),…,‘(n/n)独立同分布,借助高斯过程理论,利用第一型极值分布逼近本文所提出的变点估计量的分布,讨论了关于变点t_0,跳跃度(α2-α1)和斜率变度(β2-β1)的假设检验和区间估计问题。     

均匀分布位置参数的估计量的渐近分布及应用

对区间长度为定值均匀分布位置参数的点估计量进行了研究,得到位置参数点估计量的渐近分布.讨论了渐近分布的相关性质.给出了位置参数的区间估计及其假设检验方法.     

多源异质大数据线性模型的分布式统计推断

本文考虑多源异质大数据下线性模型的分布式统计推断问题.首先,提出针对模型参数的通信有效的分布式聚合估计及算法,并在一些正则条件下证明所得到的估计量的最优性和渐近正态性.其次,针对模型中的异质性检验问题,给出了分布式检验方法.最后,通过数值模拟研究,对本文所提出估计和检验方法的优良性进行验证.     

Admissibility of goodness of fit tests for discrete exponential families

Consider testing the composite hypothesis that a population is a particular discrete exponential family. For example, a Poisson distribution with unknown parameter. We find a sufficient condition for the admissibility of goodness of fit tests. Included in the class of admissible tests is the usual chi — square test of goodness of fit.     

Estimating functions for conditional inference: Many nuisance parameter case

When there is a complete sufficient statistic for the nuisance parameter which depends on the parameter of interest then there are locally optimal unbiased estimating functions, but generally there is no globally optimal estimating function. We consider conditioning on the minimal sufficient statistic for the nuisance parameter and find the conditional linear optimal unbiased estimating function. Since the nuisance parameter is totally eliminated in the conditional model there is no intrinsic problem in setting up conditional tests of significance and confidence intervals. A compromise between conditional and unconditional optimum estimating functions is suggested. The techniques are illustrated on three examples including the well known common means problem. The proposed hypothesis testing and confidence interval procedures work reasonably well for the examples considered.     

Empirical likelihood for balanced ranked-set sampled data

Ranked-set sampling (RSS) often provides more efficient inference than simple random sampling (SRS). In this article, we propose a systematic nonparametric technique, RSS-EL, for hypothesis testing and interval estimation with balanced RSS data using empirical likelihood (EL). We detail the approach for interval estimation and hypothesis testing in one-sample and two-sample problems and general estimating equations. In all three cases, RSS is shown to provide more efficient inference than SRS of the same size. Moreover, the RSS-EL method does not require any easily violated assumptions needed by existing rank-based nonparametric methods for RSS data, such as perfect ranking, identical ranking scheme in two groups, and location shift between two population distributions. The merit of the RSS-EL method is also demonstrated through simulation studies. This work was supported by National Natural Science Foundation of China (Grant No. 10871037)     

Testing for Uniformity of the Residual Life Time Based on Dynamic Kullback-Leibler Information

In this article a goodness of fit test for distributional assumptions regarding the residual lifetime is proposed. The test is based on a Vasicek type sum log-spacings estimators of a dynamic version of Kullback-Leibler information. The specific distributional hypothesis considered is of the uniformity over [0,1]. However, the test can be used for testing any simple goodness of fit hypothesis. The asymptotic distribution of the test statistic together with a tabulation of the critical points for different sample sizes are given. Finally, the power function of the test is empirically studied in comparison with some competitors, and the test appears to be meritorious.     

基于具有LR型模糊输出回归模型的保费预测

在保费预测研究中,提出了一种基于模糊回归模型的预测方法.采用模糊最小二乘法,针对清晰输入和LR型模糊输出,在考虑输出量隶属函数类型存在差异问题基础之上,得到模型回归系数的迭代解.通过最小二乘估计的定性分析,给出检验模型拟合度的指标.结合保费数据的预测结果表明模型可行且具有较强的解释能力.     

On the Cramér–von Mises test with parametric hypothesis for poisson processes

The problem of the goodness of-fit testing for inhomogeneous Poisson process with parametric basic hypothesis is considered. A test statistic of the Cramér–von Mises type with parameter replaced by the maximum likelihood estimator is proposed and its asymptotic behavior is studied. It is shown that in the case of shift parameter, the limit distribution of the test statistics (under hypothesis) does not depend on the true value of this parameter.     

On the use of zadeh's probabilistic definition for testing statistical hypotheses from fuzzy information

A statistical hypothesis is an assertion about the distribution of an experiment. We consider the study of the problem of testing a statistical hypothesis (that is, the problem of concluding whether or not the hypothesis is correct) on the basis of data from the experiment, when its outcomes do not provide exact but rather fuzzy information.For establishing optimality criteria of testing we will use the definition of probability of a fuzzy event, given by Zadeh, in order to extend both Neyman-Pearson and Bayes theories, to the fuzzy framework.Then, we will analyze several properties for the new criteria. Particularly, the goodness of optimal procedures in both the fuzzy and the nonfuzzy situation, will be compared for each criterion.Finally, we will apply the extended criteria for testing simple hypotheses. This application leads us to prefer Bayesian procedures to Neyman-Pearson procedures in the fuzzy context.     

The log-likelihood ratio for sparse multinomial mixtures

The log likelihood ratio is expanded for testing a sequence of multinomial null hypotheses against a sequence of multinomial mixture close alternative hypothesis. As the number of categories grows without limit, the sample size increases and the variances of the mixing distributions tend to zero. The limiting form of the log likelihood ratio is functionally different from previously studied goodness of fit statistics. The statistic derived here exhibits moderate asymptotic power when Pearson's chi-square is biased.