Gamma恒定应力加速寿命试验的统计分析

证明了基于恒定应力加速寿命试验数据Gamma模型参数的最大似然估计在一定条件下存在,进而导出了Gamma模型参数的备择估计.利用Cornish-Fisher展开导出了Gamma形状参数的近似置信区间,另外也给了Gamma模型的其它参数和正常应力水平下产品寿命的一些重要可靠性指标的广义置信区间.利用模拟方法研究了所给点估计和区间估计的精度,模拟结果显示所给点估计和区间估计的精度是相当好的.     

Stein两阶段抽样问题中第一阶段最优抽样量研究

当精度和可靠度给定时，Stein（1945）提出了两阶段抽样方法，构造了同时满足一定可靠度与精度的区间估计．本文则利用数值计算方法，进一步给出了此两阶段抽样中最优的第一阶段抽样量．     

基于置信界及信息附加寻找最大耐受剂量的逐步方法

The primary goal of a phase I clinical trial is to find the maximum tolerable dose of a treatment. In this paper, we propose a new stepwise method based on confidence bound and information incorporation to determine the maximum tolerable dose among given dose levels. On the one hand, in order to avoid severe even fatal toxicity to occur and reduce the experimental subjects, the new method is executed from the lowest dose level, and then goes on in a stepwise fashion. On the other hand, in order to improve the accuracy of the recommendation, the final recommendation of the maximum tolerable dose is accomplished through the information incorporation of an additional experimental cohort at the same dose level. Furthermore, empirical simulation results show that the new method has some real advantages in comparison with the modified continual reassessment method.     

Sequential Confidence Bands for Quantile Densities Under Truncated and Censored Data

In this paper an asymptotic distribution is obtained for the maximal deviation between the kernel quantile density estimator and the quantile density when the data are subject to random left truncation and right censorship. Based on this result we propose a fully sequential procedure for construct ing a fixed-width confidence band for the quantile density on a finite interval and show that the procedure has the desired coverage probability asymptotically as the width of the band approaches zero.     

Lincoln-Petersen模型中群体大小的置信限和置信区间

对于Lincoln-Petersen模型,基于捕获-再捕获方法得到的数据,我们给出了群体大小的置信限和置信区间的有效计算方法.     

随机套分类模型中方差分量区间估计的改进

首先给出了随机套分类模型中方差分量基于由方差分析产生的平方和的区间估计.然后以此为基础进行了改进,推导出了同时依赖于均值与平方和的区间估计.二者的区间长度相同,但后者有较高的置信度.     

双重广义线性模型的经验似然推断

基于截面经验似然方法,将双重广义线性模型的拟似然估计方程作为截面经验似然比函数的约束条件,构造了均值模型和散度模型未知参数的置信区间.最后通过数据模拟,将该方法与正态逼近方法比较,说明了该方法是有效和可行的.     

部分线性度量误差模型中的经验似然推断

部分线性度量误差模型(Partial linear measurement error model)是经典的部分线性模型的推广．在此模型中,我们假定解释变量含有度量误差．本文,我们把经验似然推广到部分线性度量误差模型,得到了非参数的Wilk's定理．我们的方法可以用来构建置信区间(域),也可以用来检验．数值模拟表明,我们的方法在构建的置信区间长度以及覆盖率方面有很好的结果．     

Empirical Likelihood Ratio Confidence Interval for Positively Associated Series

Empirical likelihood is discussed by using the blockwise technique for strongly stationary,positivelyassociated random variables.Our results show that the statistics is asymptotically chi-square distributed andthe corresponding confidence interval can be constructed.     

求参数置信限的一种方法

本文介绍一种找参数精确置信限和置信区间的一般方法,关键想法是在样本空间中定义一个序。本文主要考虑单参数统计模型，对序的优良性（即相应的置信限的优良性）作了讨论，指出应以得分函数的大小为依据在样本空间中定义序。还证明了用最大似然估计定义序得到的置信限是一个单调函数的唯一零点，从而通过解方程算出置信限。