基于混合Ⅱ型删失数据的Weibull模型精确推断和可接受抽样计划(英文)

本文考虑基于混合Ⅱ型删失数据的Weibull模型精确推断和可接受抽样计划.得到威布尔分布未知参数最大似然估计的精确分布以及基于精确分布的置信区间.由于精确分布函数较为复杂,给出未知参数的另外几种置信区间,基于近似方法的置信区间.为了评价本文的方法,给出一些数值模拟的结果.且讨论了可靠性中的可接受抽样计划问题.利用参数最大似然估计的精确分布,给出一个可接受抽样计划的执行程序和数值模拟结果.     

基于混合Ⅰ型删失数据的威布尔模型精确推断（英文）

威布尔分布是可靠性和寿命测试试验中常用的模型.本文中,我们考虑了基于混合Ⅰ型删失数据的威布尔模型精确推断.我们得到了威布尔分布未知参数最大似然估计的精确分布以及基于精确分布的置信区间.由于精确分布函数较为复杂,我们也给出了未知参数的另外几种置信区间,比如,基于近似方法的置信区间,Bootstrap置信区间.为了评价本文的方法,我们给出了一些数值模拟的结果.     

Logistic响应分布分位数的鞍点近似置信区间

论文基于响应数据，应用鞍点近似方法，给出构造Logistic响应分布分位数的近似置信区间的方法. 论文还对这种置信区间进行了模拟，并将该方法应用于QD8电雷管. 模拟和实例结果表明，当样本量较小时，该方法能够较好地推断Logistic响应分布的分位数     

多元比例响应数据的贝叶斯推断及其应用

多元比例响应数据具有有界性、归一性以及分量取值稀疏性等特点。本文在多项分布拟似然框架下基于贝叶斯方法研究多元比例数据的估计及其推断问题。通过引入Polya-Gamma分布的潜在变量,得到了易于后验抽样的Gibbs抽样算法。新方法具有估计稳健性、计算量小、推断效率高等特点,且不需要事先对响应数据作近似或变换。大量的数值模拟分析和两个实例分析验证了所提方法的有效性。     

基于循序-Ⅰ型删失数据的Gompertz-sinh分布的统计推断(英文)

本文研究在循序-I型删失数据情形下Gompertz-sinh分布的统计推断问题.利用处理删失数据的EM算法,讨论Gompertz-sinh分布未知参数的最大似然估计(MLE)问题.为了讨论未知参数的近似置信区间估计,基于遗失信息原则,给出观测Fisher信息矩阵.为了演示本文的方法,给出相关数值模拟结果和一个真实数据实例.     

基于循序-I型删失数据的Gompertz-sinh分布的统计推断[英文]

本文研究了在循序-I型删失数据情形下Gompertz-sinh分布的统计推断问题.利用处理删失数据的EM算法,我们讨论了Gompertz-sinh分布未知参数的最大似然估计(MLE)问题.为了讨论未知参数的近似置信区间估计,基于遗失信息原则,我们给出了观测Fisher信息矩阵.为了演示本文的方法,我们给出了相关数值模拟结果和一个真实数据实例.     

关于截断中值回归模型的经验似然推断

本文采用了Gengsheng和Min(2003)提出的经验似然方法,基于一个新的方程对中值回归模型的参数进行统计推断,数值模拟的结果表明,本文所得到的参数估计结果比Gengsheng和Min(2003)的模拟结果更精确.     

基于联合II型删失数据的两总体指数模型的精确统计推断（英文）

在本文中,我们讨论两指数总体的位置参数和尺度参数的统计推断问题.利用极大似然方法,在联合II型删失数据的情形下给出参数的精确分布以及相关精确统计推断结果.将枢轴量表示为标准指数随机变量的线性函数,并且给出枢轴量的条件精确分布,这个条件精确分布的一个很大优点是计算比较简单.利用条件精确分布,可以获得枢轴量的精确分位数.为了说明本文方法的优劣,我们也提供Bootstrap方法构造参数置信区间的相关结果.最后将理论结果,进行了部分数值模拟实验,这些数值结果列在相应的表格里.     

基于分组数据的指数分布参数的同变估计

给出了基于分组数据的指数分布参数的同变估计,其中位置参数是最优同变估计,刻度参数为近似最优同变估计,最后通过Monte-Carlo模拟数据说明方法的可行性.     

三参数WEIBULL分布的统计推断

本文给出了三参数Ｗｅｉｂｕｌｌ分布在定数截尾下求参数点估计的一种新方法，模拟结果表明其精度比原有估计更高，同时本文还给出了求位置参数置人下降的一种新方法，且精度比过去的方法更高，包括的信息量也更多。文章还给出了基于位置参数点估计为求形状参数，刻度参数的区间估计以及可靠度的置信下降，失效率的置信上限的方法，通过大量的模拟说明了其方法是可行的。     

核实数据下响应变量缺失的线性EV模型经验似然推断

考虑响应变量随机缺失而协变量带有误差的线性模型,借助于核实数据和借补方法,构造了回归系数的两种经验似然比,证明了所提出的估计的经验对数似然比渐近于一个自由度为1的独立χ2变量的加权和;而经调整后所得的调整经验对数似然比渐近于自由度为p的χ2分布,该结果可以用来构造未知参数的置信域.此外,我们也构造了响应均值的调整经验对数似然比统计量,并证明了所提出的统计量渐近于x2分布,可用此结果构造响应均值的置信域.通过模拟研究比较了置信域的精度及其平均区间长度.     

Generalized fiducial confidence intervals for extremes

The generalized Pareto distribution is relevant to many situations when modeling extremes of random variables. In particular, peaks over threshold data approximately follow the generalized Pareto distribution. We use a fiducial framework to perform inference on the parameters and the extreme quantiles of the generalized Pareto. This inference technique is demonstrated both when the threshold is a known and unknown parameter. Assuming the threshold is a known parameter resulted in fiducial intervals with good empirical properties and asymptotically correct coverage. Likewise, our simulation results suggest that the fiducial intervals and point estimates compare favorably to the competing methods seen in the literature. The proposed intervals for the extreme quantiles when the threshold is unknown also have good empirical properties regardless of the underlying distribution of the data. Comparisons to a similar Bayesian method suggest that the fiducial intervals have better coverage and are similar in length with fewer assumptions. In addition to simulation results, the proposed method is applied to a data set from the NASDAQ 100. The data set is analyzed using the fiducial approach and its competitors for both cases when the threshold is known and unknown. R code for our procedure can be downloaded at .     

Likelihood ratio inference for mean residual life of length-biased random variable

In lifetime data analysis, naturally recorded observations are length-biased data if the probability to select an item is proportional to its length. Based on i.i.d. observations of the true distribution, empirical likelihood (EL) procedure is proposed for the inference on mean residual life (MRL) of naturally recorded item. The limit distribution of the EL based log-likelihood ratio is proved to be the chi-square distribution. Under right censorship, since the EL based log-likelihood ratio leads to a scaled chi-square distribution and estimating the scale parameter leads to lower coverage of confidence interval, we propose an algorithm to calculate the likelihood ratio (LR) directly. The corresponding log-likelihood ratio converges to the standard chi-square distribution and the corresponding confidence interval has a better coverage. Simulation studies are used to support the theoretical results.     

Efficient empirical-likelihood-based inferences for the single-index model

This article proposes the efficient empirical-likelihood-based inferences for the single component of the parameter and the link function in the single-index model. Unlike the existing empirical likelihood procedures for the single-index model, the proposed profile empirical likelihood for the parameter is constructed by using some components of the maximum empirical likelihood estimator (MELE) based on a semiparametric efficient score. The empirical-likelihood-based inference for the link function is also considered. The resulting statistics are proved to follow a standard chi-squared limiting distribution. Simulation studies are undertaken to assess the finite sample performance of the proposed confidence intervals. An application to real data set is illustrated.     

Empirical likelihood inference for the accelerated failure time model

Accelerated failure time (AFT) models are useful regression tools for studying the association between a survival time and covariates. Semiparametric inference procedures have been proposed in an extensive literature. Among these, use of an estimating equation which is monotone in the regression parameter and has some excellent properties was proposed by Fygenson and Ritov (1994). However, there is a serious under-coverage problem for small sample sizes. In this paper, we derive the limiting distribution of the empirical log-likelihood ratio for the regression parameter on the basis of the monotone estimating equations. Furthermore, the empirical likelihood (EL) confidence intervals/regions for the regression parameter are obtained. We conduct a simulation study in order to compare the proposed EL method with the normal approximation method. The simulation results suggest that the empirical likelihood based method outperforms the normal approximation based method in terms of coverage probability. Thus, the proposed EL method overcomes the under-coverage problem of the normal approximation method.     

缺失数据下半参数回归模型的经验似然推断

针对响应变量缺失下的半参数回归模型,构造模型中未知参数的经验对数似然比统计量,证明了所提出的统计量具有渐近χ2分布,由此构造未知参数的置信域,并就置信域的覆盖概率及区间长度方面,通过模拟研究与最小二乘法进行优劣比较.     

位置刻度分布族中参数的两步置信区间

寻找一些分布中的参数的具有预先给定宽度和预先给定覆盖概率的置信区间是令人感兴趣的，对于位置刻度分布族中位置参数和刻度参数，这种类型的置信区间的存在性问题已在文献中被解决，本文利用两步抽样，具体地构造出这样的固定宽度置信区间，此外，对于Cauchy分布，第一阶段的最优抽样量和一些统计量的分位点也被计算出，所得到的结果具有应用价值。