Wilcoxon signed rank test using ranked-set sample

Ranked-set sampling is useful when measurements are destructive or costly to obtain but ranking of the observations is relatively easy. The Wilcoxon signed rank test statistic based on the ranked-set sample is considered. We compared the asymptotic relative efficiencies of the RSS Wilcoxon signed rank test statistic with respect to the SRS Wilcoxon signed rank test statistic and the RSS sign test statistic. Throughout the ARE’s, the proposed test statistic is superior to the SRS Wilcoxon signed rank test statistic and the RSS sign test statistic.     

Competitors of the Wilcoxon signed rank test

Summary Distribution-free statistics are proposed for one-sample location test, and are compared with the Wilcoxon signed rank test. It is shown that one of the statistics is superior to the Wilcoxon test in terms of approximate Bahadur efficiency. And we compare that statistic with the Wilcoxon test from the viewpoint of asymptotic expansion of power function under contiguous alternatives.     

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。     

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The definition of Brownian distance is presented and it's proved that Brownian distance coincides with the energy distance with respect to Brownian motion. Energy distance for dependent random vectors is also given and the asymptotic distribution is derived under null hypothesis. A simple numerical simulation result shows that the method for paired-sample test based on energy distance can distinguish the distributions of the paired variables more effectively than the classical t-test and Wilcoxon signed rank test.     

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.     

Asymptotically efficient two-sample rank tests for modal directions on spheres

A general class of optimal and distribution-free rank tests for the two-sample modal directions problem on (hyper-) spheres is proposed, along with an asymptotic distribution theory for such spherical rank tests. The asymptotic optimality of the spherical rank tests in terms of power-equivalence to the spherical likelihood ratio tests is studied, while the spherical Wilcoxon rank test, an important case for the class of spherical rank tests, is further investigated. A data set is reanalyzed and some errors made in previous studies are corrected. On the usual sphere, a lower bound on the asymptotic Pitman relative efficiency relative to Hotelling’s T²-type test is established, and a new distribution for which the spherical Wilcoxon rank test is optimal is also introduced.     

Inference for a simple step-stress model based on ordered ranked set sampling

In this paper, we considered the inference problem on simple step-stress accelerated life test data from one-parameter exponential distribution under type-I censored ordered ranked set sample with cumulative exposure model. The Bayesian estimators and credible intervals for the model parameters are developed and compared with the corresponding estimators based on simple random sampling. Two real data sets and numerical simulation evaluations are presented to illustrate all the results developed here. The simulation study indicated that the proposed Bayes estimators and credible intervals based on ordered ranked set sampling performed better than their counterparts using simple random sampling.     

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。     

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.     

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.     

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.     

基于非参数方法的DNA序列信噪比阈值研究

基于人类、鼠类及其他哺乳动物的基因数据,共计1264个外显子、1553个内含子进行基因预测,对DNA序列信噪比阈值进行判断.提出基于Mann-Whitney检验、符号检验、Wilcoxon符号秩和检验的非参数置信区间法计算信噪比阈值,得到人类的阈值为1.108,鼠类的为1.0971,其他哺乳动物的为1.1754,与均值平均法、带标准差加权平均法、定义阈值为2的方法比较判断的正确率,结果表明利用非参数置信区间法计算的阈值在基因预测中具有最高的正确率.     

Local powers of two-sample and multi-sample rank tests for Lehmann's contaminated alternative

Summary Local powers of two- andk-sample rank tests under alternatives of contaminated distributions are investigated. It is shown that the rank tests based on normal scores and Wilcoxon scores are superior to thet-test or theF-test for many choices of alternatives of contaminated distributions and that the values of the asymptotic relative efficiency of the rank test based on Wilcoxon scores with respect to the normal scores are about one in all the investigated cases.     

An example of a two-sided Wilcoxon signed rank test which is not unbiased

Although the theory of rank tests is rather complete in the one-sided case, it was not even known in 1959, whether the Wilcoxon two-sample test and other similar tests are unbiased against the two-sided alternatives (Lehmann (1959,Testing Statistical Hypotheses, p. 240, Wiley, New York)). A partial answer to this question was given by Sugiura in 1965, who found, that the test named above may be biased (Sugiura (1965,Ann. Inst. Statist. Math.,17, 261–263)). According to Lehmann (1986,Testing Statistical Hypotheses, 2nd ed., pp. 322–324, Wiley, New York) it seems to be still open, whether the same is true for the WILCOXON one-sample test, which is also known as WILCOXON signed rank test. This will be shown in the present paper.     

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.     

On multivariate signed rank tests

Summary As a test for the hypothesis of equality of means in a sample ofn matched pairs of observations from a single bivariate population in(x, y), Wilcoxon ([4], [5]) proposed a signed rank sum testU involving the differencesz=x\t-y. Tables of valuesUs have been provided forn of 50 or less and four significance levelsε. The following paper considers some generalizations of the Wilcoxon test for the case of matched bivariate or trivariate populations. These tests utilize certain properties of thep-variate normal distribution when integrated over certain regions for the cases:p=2,3.     

Biased and Unbiased Two-sided Wilcoxon Tests for Equal Sample Sizes

This paper answers the long-standing question of whether the two-sided Wilcoxon rank test for equal sample sizes is unbiased against a location parameter family of distributions by giving a counterexample. It is also shown that the nonrandomized two-sided Wilcoxon test for equal sample sizes with the least positive significance level is unbiased.     

Robustness to Non-Normality of Various Tests For the One-Sample Location Problem

This paper studies the effect of the normal distribution assumption on the power and size of the sign test, Wilcoxon's signed rank test and the t-test when used in one-sample location problems. Power functions for these tests under various skewness and kurtosis conditions are produced for several sample sizes from simulated data using the g-and-k distribution of MacGillivray and Cannon [5].     

Smoothed nonparametric tests and approximations of <Emphasis Type="Italic">p</Emphasis>-values

We propose new smoothed sign and Wilcoxon’s signed rank tests that are based on kernel estimators of the underlying distribution function of the data. We discuss the approximations of the p-values and asymptotic properties of these tests. The new smoothed tests are equivalent to the ordinary sign and Wilcoxon’s tests in the sense of Pitman’s asymptotic relative efficiency, and the differences between the ordinary and new tests converge to zero in probability. Under the null hypothesis, the main terms of the asymptotic expectations and variances of the tests do not depend on the underlying distribution. Although the smoothed tests are not distribution-free, making use of the specific kernel enables us to obtain the Edgeworth expansions, being free of the underlying distribution.     

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.