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.     

Exact two-sample nonparametric test for quantile difference between two populations based on ranked set samples

Creation of a ranked set sample, by its nature, involves judgment ranking error within set units. This ranking error usually distorts statistical inference of the population characteristics. Tests may have inflated sizes, confidence intervals may have incorrect coverage probabilities, and the estimators may become biased. In this paper, we develop an exact two-sample nonparametric test for quantile shift between two populations based on ranked set samples. This test is based on two independent exact confidence intervals for the quantile of interest corresponding to the two populations and rejects the null hypothesis of equal quantiles if these intervals are disjoint. It is shown that a pair of 83 and 93% confidence intervals provide a 5 and 1% test for the equality of quantiles. The proposed test is calibrated for the effect of judgment ranking error so that the test has the correct size even under a wide range of judgment ranking errors. A small scale simulation study suggests that the test performs quite well for cycle sizes as small as 2.     

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.     

Asymptotically efficient rank MANOVA tests for restricted alternatives in randomized block designs

In a randomized block design MANOVA model, for intrablock as well as aligned rank tests for homogeneity of treatment effects against some restricted alternatives, asymptotic optimality is studied by reference to the corresponding restrieted likelihood ratio tests. Tests based on aligned ranks are better than intra-block rank tests when the error distributions are homogeneous aeross the blocks.Work of this author was partially supported by the Office of Naval Research, Contract No. N00014-83-K-0987.     

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.     

Estimation of the Common Mean of a Bivariate Normal Population

In this paper we discuss the problem of estimating the common mean of a bivariate normal population based on paired data as well as data on one of the marginals. Two double sampling schemes with the second stage sampling being either a simple random sampling (SRS) or a ranked set sampling (RSS) are considered. Two common mean estimators are proposed. It is found that under normality, the proposed RSS common mean estimator is always superior to the proposed SRS common mean estimator and other existing estimators such as the RSS regression estimator proposed by Yu and Lam (1997, Biometrics, 53, 1070–1080). The problem of estimating the mean Reid Vapor Pressure (RVP) of regular gasoline based on field and laboratory data is considered.     

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.     

3阶不可约符号模式的精细惯量极小临界集

Let S be a nonempty, proper subset of all possible refined inertias of real matrices of order n. The set S is a critical set of refined inertias for irreducible sign patterns of order n,if for each n × n irreducible sign pattern A, the condition S ? ri(A) is sufficient for A to be refined inertially arbitrary. If no proper subset of S is a critical set of refined inertias, then S is a minimal critical set of refined inertias for irreducible sign patterns of order n.All minimal critical sets of refined inertias for full sign patterns of order 3 have been identified in [Wei GAO, Zhongshan LI, Lihua ZHANG, The minimal critical sets of refined inertias for 3×3 full sign patterns, Linear Algebra Appl. 458(2014), 183–196]. In this paper, the minimal critical sets of refined inertias for irreducible sign patterns of order 3 are identified.     

On the construction of restricted minimum aberration designs

Deriving a formula, we show that an optimal moment design has the property that each treatment combination appears as equally often as possible. Modifying the definition of minimum aberration to restricted minimum aberration, we show that the word length pattern of a design is proportional to that of its complement. Many restricted minimum aberration designs are constructed.     

On tight projective designs

It is shown that among all tight designs in , where is or , or (quaternions), only 5-designs in (Lyubich, Shatalora Geom Dedicata 86: 169–178, 2001) have irrational angle set. This is the only case of equal ranks of the first and the last irreducible idempotent in the corresponding Bose-Mesner algebra.      

排序集抽样下Inverse Rayleigh分布的Fisher信息量及其在参数估计中的应用

文章分别在简单随机抽样和排序集抽样下研究了Inverse Rayleigh分布中对应样本所含刻度参数θ的Fisher信息量.数值结果表示,同等样本容量的排序集样本比简单随机样本提供更多关于θ的信息.接着分别基于简单随机样本和排序集样本构造了θ的一些优良估计,并对估计结果进行了数值比较.     

D‐optimal designs and group divisible designs

We obtain new conditions on the existence of a square matrix whose Gram matrix has a block structure with certain properties, including D‐optimal designs of order , and investigate relations to group divisible designs. We also find a matrix with large determinant for n = 39. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 451–462, 2006     

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.     

均匀设计抽样的一、二阶矩

（７）中给出并研究了均匀设计抽样（ＵＤＳ）及随机化均匀设计（ＲＵＤ）的一些优良性质,作者给出该设计和抽样的一、二阶矩。     

Comments on 3‐blocked designs

This note provides a correction and some additions to a 1999 article by Luigia Berardi and Fulvio Zuanni on blocking 3‐sets in designs. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 328–331, 2012     

基于有序抽样样本的参数的极大似然估计的性质

有序抽样是一种新的抽样方法 ,与简单随机抽样方法相比它具有很多很好的性质 .本文讨论了在有序抽样样本下的参数的极大似然估计的性质 .     

Primitive symmetric designs with prime power number of points

In this paper we either prove the non‐existence or give explicit construction of primitive symmetric (v, k, λ) designs with v=p^m<2500, p prime and m>1. The method of design construction is based on an automorphism group action; non‐existence results additionally include the theory of difference sets, multiplier theorems in particular. The research involves programming and wide‐range computations. We make use of software package GAP and the library of primitive groups which it contains. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 141–154, 2010     

Block designs which are divisible in multiple ways

Constructions are given for the production of symmetric block designs whose point set is divisible (partitionable) in several ways. Some properties of the dual design are also considered. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 415–422, 2006     

Practical tests for randomized complete block designs

A class of affine-invariant test statistics, including a sign test and a related family of signed-rank tests, is proposed for randomized complete block designs with one observation per treatment. This class is obtained by using the transformation-retransformation approach of Chakraborty, Chaudhuri and Oja along with a directional transformation due to Tyler. Under the minimal assumption of directional symmetry of the underlying distribution, the null asymptotic distribution of the sign test statistic is shown to be chi-square with p-1 degrees of freedom. The same null distribution is also proved for the family of signed-rank statistics under the assumption of symmetry of the underlying distribution. The Pitman asymptotic relative efficiencies of the tests, relative to Hotelling-Hsu's T² are established. Several score functions are discussed including a simple linear score function and the optimal normal score function. The test based on the linear score function is compared to the other members of this family and other statistics in the literature through efficiency calculations and Monte Carlo simulations. This statistic has an excellent performance over a wide range of distributions and for small as well as large dimensions.