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.     

序集抽样中$M$估计分布的随机加权逼近

序集抽样是一种适用于准确测量花费太高而排序费用可以忽略不记时的一种抽样方法.讨论了序集抽样下的对于一般分布族M估计的相合性和渐近正态性并且通过随机加权的方法来估计M估计的分布.     

一种基于因素空间理论的群体整体优势的投影评价模型与实证

群体对象的多因素综合评价问题的数学本质是多元数据集合的排序问题,藉此确定群体间的相对优势.本文基于多因素轮廓分析的概念与方法,建立了多元数据集合到一维数据集合无信息损失的非线性投影方法.基于经典集合论,定义了集合的稀疏特征和分布特征,建立了一维数据集合优势关系的比对算法.在比对矩阵的基础上给出了多元数据集合间的排序模型.最后在UCI共享User Knowledge Modeling数据集上,对算法的有效性进行了实证分析.     

两台单机的合作排序问题北大核心CSCD

本文研究下面情形的排序问题,两个代理商联合加工来自客户的一个工件集,每个代理商仅有一台单机用于加工工件,每个工件仅需被其中的一台单机无中断地加工一次.在完成分配工件的加工任务后,每个代理商将获得一定的收益并付出一定的加工费用.需要找出工件集的一个最优划分,使得两个代理商的净收益乘积最大.本文研究三个不同经典排序目标作为加工费用的两机合作排序模型,证明模型复杂性,分析最优解结构并设计动态规划算法.     

两台单机的合作排序问题

本文研究下面情形的排序问题,两个代理商联合加工来自客户的一个工件集,每个代理商仅有一台单机用于加工工件,每个工件仅需被其中的一台单机无中断地加工一次.在完成分配工件的加工任务后,每个代理商将获得一定的收益并付出一定的加工费用.需要找出工件集的一个最优划分,使得两个代理商的净收益乘积最大.本文研究三个不同经典排序目标作为加工费用的两机合作排序模型,证明模型复杂性,分析最优解结构并设计动态规划算法.     

考虑属性关联的C-TODIM决策方法

针对属性具有关联性的多属性决策问题,考虑到决策者具有参照依赖和损失规避行为,提出一种新的C-TODIM决策方法。依据经典TODIM决策方法,考虑决策者的参照依赖行为,计算每个方案相对于其它各个方案关于各属性的收益或损失值;再考虑到决策者的损失规避行为,集成属性关联情形下方案关于所有属性的收益或损失值,得到每个方案相对于其它各个方案的个体感知优势度;在此基础上,计算每个方案的总体感知优势度,并依据总体感知优势度的大小对方案进行排序。最后通过一个风险投资的算例验证该方法的可行性和有效性。     

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.     

考虑决策者心理行为的直觉语言多属性决策方法

针对应用直觉语言集来表达决策信息的语言多属性决策问题,在考虑决策者有限理性的心理行为基础上,提出一种决策方法。该方法通过比较每个属性下方案之间的得分函数和精确函数, 构建方案的收益-损失分析矩阵。在考虑决策者参照依赖和损失规避心理行为基础上,计算每个方案相对于其它方案在每个属性下的收益-损失值优先度;在此基础上,计算备选方案的综合优先度, 并根据其大小对方案进行排序择优。最后通过一个算例验证所提出方法的有效性和合理性。     

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。     

一种可供选择的随机化调查方法

本文提出了一种新的随机化调查方法,Warner(1965)和Horvitz,Simmons(1967)随机化回答方法是本文方法的特殊情形.这一方法比Warner(1965)方法和Mangat(1990)方法更有效. 当考虑存在不真实回答时,在一定的条件下并且不损失对个体保护度和不增加调查成本的前提下,提出的方法优于Simmons(1967)方法和Sarjinder Singh(2000)方法.对简单随机不放回抽样,在总体非敏感属性个体比例未知的情况下,给出了两个子样本容量的最优配置.     

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。     

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.     

Parametric estimation for the simple linear regression model under moving extremes ranked set sampling design

Cost effective sampling design is a major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time consuming.Ranked set sampling(RSS) was first proposed by McIntyre [1952. A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research 3, 385-390]as an effective way to estimate the pasture mean. In the current paper, a modification of ranked set sampling called moving extremes ranked set sampling(MERSS) is considered for the best linear unbiased estimators(BLUEs) for the simple linear regression model. The BLUEs for this model under MERSS are derived. The BLUEs under MERSS are shown to be markedly more efficient for normal data when compared with the BLUEs under simple random sampling.     

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。     

Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling

Ranked set sampling is applicable whenever ranking of a set of sampling units can be done easily by a judgement method or based on the measurement of an auxiliary variable on the units selected. In this work, we consider ranked set sampling, in which ranking of units are done based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. We then estimate the mean of the study variate Y by the BLUE based on the measurements made on the units of the ranked set sampling regarding the study variable Y, when (X ,Y) follows a Morgenstern type bivariate exponential distribution. We then consider unbalanced multistage ranked set sampling and estimate the mean of the study variate Y by the BLUE based on the observations made on the units of multistage ranked set sample regarding the study variable Y. Efficiency comparison is also made on all estimators considered in this work.     

Order restricted randomized designs for control versus treatment comparison

We develop a method of randomizing units to treatments that relies on subjective judgement or on possible coarse modeling to produce restrictions on the randomization. The procedure thus fits within the general framework of ranked set sampling. However, instead of selecting a single unit from each set for full measurement, all units within a set are used. The units within a set are assigned to different treatments. Such an assignment translates the positive dependence among units within a set into a reduction in variation of contrasting features of the treatments. A test for treatment versus control comparison, with controlled familywise error rate, is developed along with the associated confidence intervals. The new procedure is shown to be superior to corresponding procedures based on completely randomized or ranked set sample designs. The superiority appears both in asymptotic relative efficiency and in power for finite sample sizes. Importantly, this test does not rely on perfect rankings; rather, the information in the data on the quality of rankings is exploited to maintain the level of the test when rankings are imperfect. The asymptotic relative efficiency of the test is not affected by estimation of the quality of rankings, and the finite sample performance is only mildly affected.     

Sign tests using ranked set sampling with unequal set sizes

This paper considers sign test under ranked set sampling with unequal set sizes (RSSU), and proposes weighted sign tests associated with judgment ranks. The optimal weight vector is shown to be distribution-free, and RSSU is shown to be more efficient than ranked set sampling.     

优良抽样设计下Logistic分布中参数的极大似然估计

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(RSS)被视为一种比简单随机抽样(SRS)更为有效的收集数据的方式.动态极值RSS (MERSS)是一种修正的RSS.文章在SRS和MERSS下研究了Logistic分布中参数的极大似然估计(MLEs).在这两种抽样下证明了该分布中位置参数和刻度参数的MLEs的存在性和唯一性,并计算了所含参数的Fisher信息量和Fisher信息矩阵.比较了这两种抽样下对应估计的渐近效率.数值结果表明MERSS下的MLEs一致优于SRS下的MLEs.     

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.     

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.