产品可靠寿命的最优排序集挑选设计

针对产品可靠寿命的估计问题,构造了基于排序集挑选样本的非参数估计量,证明了该估计量具有强相合性和渐近正态性。针对不同的可靠寿命,具体给出了使得估计效率达到最大的最优挑选抽样设计。最后,渐近相对效率和实际应用的研究结果表明:最优挑选设计的抽样效率高于简单随机抽样。     

基于排序集抽样的非参数推断

主要考虑基于排序集抽样的两样本刻度参数检验，以Mood统计量为核，构造了两样本U统计量，并得出相应的极限分布，在总体分布为均匀分布的情况下，讨论了此检验统计量相对于Mood检验统计量的渐近效率．     

符号检验的最优排序集抽样(英文)

提出检验总体分位数的基于排序集抽样的符号检验,分析了不同挑选抽样相对于均衡抽样的Pitman渐近效率.针对不同分位数,具体给出使符号统计量的效率达到最大的抽样设计,并且证明了最优抽样不依赖于总体分布.     

基于中位数排序集抽样的非参数估计

本文提出中位数排序集抽样下总体中位数的非参数估计,证明了这种估计具有强相合性和渐近正态性,并系统验证了新估计量的功效一致优于排序集抽样下和简单随机抽样下总体中位数的估计量。最后,我们对针叶树的一组真实数据进行了实际应用。     

排序集抽样下指数分布参数的最优线性无偏估计

排序集抽样方法适用于样本测量困难但排序容易的场合,其样本包含了次序信息.指数分布在寿命试验中占有非常重要的地位,为了提高指数分布参数的估计效率,本文提出了排序集抽样下参数的最优线性无偏估计量,计算了新估计量的方差,证明了其具有渐近正态性.相对效率和模拟效率的研究结果表明:新估计量的估计效率不仅高于简单随机抽样下一致最小方差无偏估计量,也高于排序集抽样下样本均值和修正极大似然估计量.最后,将推荐方法应用到转移性肾癌的临床研究中,从而验证该方法的有效性.     

基于样本均值的最优无重叠k-序对排序集抽样

本文提出了无重叠κ-序对排序集抽样方法,即在每个排序集中对κ-序对个体进行观测,并且不同的排序集的κ-序对之间没有任何重复.我们首先探究了此抽样方法得到的样本均值的有效性随每个排序集中κ-序对个体间的相关性变化的趋势.κ-序对个体间的相关性越强,样本均值的有效性损失越大.本文的目的是找到无重叠κ-序对排序集抽样方法中κ-序对分配的最优方案从而使样本均值的有效性损失最小,并证明了最优的无重叠κ-序对排序集抽样比广义排序集抽样以及简单随机抽样更有效.尽管无重叠κ-序对排序集抽样方法的统计效率低于经典的排序集抽样,但是在成本模型下,最优的无重叠κ-序对排序集抽样方法可以比经典的排序集抽样更有效.     

一种新的中位数排序集抽样下的对总体均值的Horvitz-Thompson估计

排序集抽样(RSS)是一种著名的抽样技术,它有许多变体,中位数排序集抽样(MRSS)就是其中一种.与简单随机抽样(SRS)相比,RSS在估计总体均值方面具有优势.然而,RSS及其变体的局限性在于,当给定样本大小n时,抽样过程中每次SRS的规模m只能是n或者n的因子.介绍了一种改进的中位数排序集抽样方法MRSS(m),它比原方法在抽样过程上有更多的选择.实验表明,采用新的抽样方法MRSS(m),可以提高Horvitz-Thompson(HT)估计量的估计效率,同时还降低了抽样成本.     

不完美排序集抽样的符号检验

实际应用排序集抽样时,主观排序总是会出现误差。本文考虑了不完美排序对最优抽样下分位数符号检验的影响,并且给出不同分位数的误差函数图像,以便具体应用时参考。     

对称分布下中位数排序集样本均值的有效性证明

总体均值的估计在整个抽样理论里扮演着无可争议的主角,而估计的好坏很大程度上依赖于抽样设计.文章从理论上证明了在对称分布下,基于中位数排序集抽样的样本均值作为总体均值的估计比简单随机抽样下样本均值作为总体均值的估计更有效.小样本情形下的两个数值例子和一个实例进一步验证了这个理论结果.     

基于辅助信息的分层排序集抽样及调查费用分析

辅助信息在改进和完善抽样设计、提高抽样估计精度和节省抽样费用等方面具有重要作用,鉴于此,基于分层排序集样本建立了总体均值的比率估计量,同时考虑估计精度和调查费用两个方面,证明了抽样方案的优良性.最后,通过实例进一步分析,结果表明,在给定的估计精度下,分层排序集抽样方法可以有效降低抽样调查费用.     

Modified Maximum Likelihood Estimators Based on Ranked Set Samples

The maximum livelihood estimator (MLE) using a ranked set sample (RSS) usually has no closed expression because the maximum likelihood equation involves both hazard and inverse hazard functions, and may no longer be efficient when the judgment ranking is imperfect. In this paper, we consider a modified MLE (MMLE) using RSS for general parameters, which has the same expression as the MLE using a simple random sample (SRS), except that the SRS in the MLE is replaced by the RSS. The results show that, for the location parameter, the MMLE is always more efficient than the MLE using SRS, and for the scale parameter, the MMLE is at least as efficient as the MLE using SRS, when the same sample size is used. Under the perfect judgment ranking, numerical examples also show that the MMLE has good efficiency relative to the MLE based on RSS. When the judgment error is present, we conduct simulations to show that the MMLE is more robust than the MLE using RSS.     

排序集抽样下指数分布的产品可靠度研究

为了提高指数分布产品可靠度的估计效率,研究了基于排序集抽样方法的极大似然估计量(Maximum likelihood estimator,MLE),证明了新MLE具有存在性、唯一性和渐近正态性,并通过排序集样本的Fisher信息得到MLE的渐近方差。针对似然方程没有显式解的问题,利用部分期望法对MLE进行修正,并给出其具体表达式。渐近相对效率和模拟相对效率的研究结果表明:排序集抽样下MLE和修正MLE的估计效率都一致高于简单随机抽样下MLE。最后,将推荐方法应用到转移性肾癌的临床研究中。     

Dependence Between Order Statistics in Samples from Finite Population and its Application to Ranked Set Sampling

Let X1, X2,..., Xm, Y1, Y2,..., Yn be a simple random sample without replacement from a finite population and let X(1) X(2) ... X(m) and Y(1) Y(2) ... Y(n) be the order statistics of X1, X2,..., Xm and Y1, Y2,..., Yn, respectively. It is shown that the joint distribution of X(i) and X(j) is positively likelihood ratio dependent and Y(j) is negatively regression dependent on X(i). Using these results, it is shown that when samples are drawn without replacement from a finite population, the relative precision of the ranked set sampling estimator of the population mean, relative to the simple random sample estimator with the same number of units quantified, is bounded below by 1.     

优良抽样设计下总体均值的比率估计

当研究目标的实际测量具有不可修复的破坏性或耗资巨大时,有效的抽样设计将是一项重要的研究课题.在统计推断方面,排序集抽样被视为一种更为有效的收集数据的方式.极值排序集抽样(ERSS)是一种改进的排序集抽样.文章在ERSS下研究了总体均值的比率估计.以正态分布为例,比较了简单随机抽样和ERSS下比率估计的相对效率.数值结果表明ERSS下的比率估计优于简单随机抽样下的比率估计.     

Optimal Allocation for Symmetric Distributions in Ranked Set Sampling

Ranked set sampling (RSS) is a cost efficient method of sampling that provides a more precise estimator of population mean than simple random sampling. The benefits due to ranked set sampling further increase when appropriate allocation of sampling units is made. For highly skew distributions, allocation based on the Neyman criterion achieves a substantial precision gain over equal allocation. But the same is not true for symmetric distributions; in fact, the gains due to using the Neyman allocation are typically very marginal for symmetric distributions. This paper, determines optimal RSS allocations for two classes of symmetric distributions. Depending upon the class, the optimal allocation assigns all measurements either to the extreme ranks or to the middle rank(s). This allocation outperforms both equal and Neyman allocations in terms of the precision of the estimator which remains unbiased. The two classes of distributions are distinguished by different growth patterns in the variance of their order statistics regarded as a function of the rank order. For one class, the variance peaks for middle rank orders and tapers off in the tails; for the other class, the variance peaks for the two extreme rank orders and tapers off toward the middle. Kurtosis appears to effectively discriminate between the two classes of symmetic distributions. The Neyman allocation is required to quantify all rank orders at least once (to ensure general unbiasedness) but then quantifies most frequently the more variable rank orders. Under symmetry, unbiasedness can be obtained without quantifying all rank orders and the optimal allocation quantifies the least variable rank order(s), resulting in a high precision estimator.