基于排序集抽样方法的调查费用分析

排序集抽样是利用辅助信息收集数据的一种有效方法,基于该抽样方法进行统计推断越来越受到人们的重视。然而,已有的研究结果仅考虑统计推断的效率而忽视了调查费用,鉴于此,文章考虑估计精度和调查费用两个方面,基于排序集样本建立了总体均值的估计量,证明了该估计量在给定的估计的精度下,降低了调查费用,并通过实例进一步说明了该抽样方案的优良性。     

分层抽样下的样本轮换理论研究

讨论用于回归估计的二相抽样理论在分层抽样下样本轮换后估计量的构造及其精度问题，并在构造的估计量的基础上计算了分层抽样下的最优样本轮换率，这对于深入研究分层抽样理论，使其估计量的精度提高，从而更好地实现抽样调查的目标有积极意义。     

基于分层设计效应的样本分配研究

文章从分层抽样的角度,以设计效应为工具,构造出若干种分层抽样的设计效应模型,应用于分层抽样的样本分配设计.由于分层设计效应主要取决于各层平均数的差异,则差异越大,分层的效果越好.为了满足目标变量全国估计量和特定小域估计量的精度要求,样本在各小域的最优分配可能是比例分配和非比例分配的折中.     

分层排序集抽样下的比率估计问题探讨

分层排序集抽样是指将分层抽样与排序集抽样结合起来,运用分层技术将总体分为多层,再在每层中用排序集抽样获取样本.分层比率估计是利用辅助信息,构造总体均值或总值的估计量,分为联合比率估计和分别比率估计.文章利用此思路得到下分层排序集抽样下总体均值的分别比率估计,并和分层排序集抽样下的联合比率估计、分层随机抽样下的分别比率估计进行比较.结果表明,分层排序集抽样下总体均值的分别比率估计比分层随机抽样下总体均值的分别比率估计效果好,分层排序集抽样下总体均值的联合比率估计比分层排序集抽样下总体均值的分别比率估计效果好.     

分层抽样样本量最优分配问题新探

一、问题的提出 在分层抽样中涉及到样本量最优化分配的问题.样本分配是分层抽样研究的一个重要方面.一般来说,一个恰当的分层的原则是这样的:确定各层的样本容量,使样本容量的分布趋于总体分布,以保证样本具有充分代表性,抽样估计准确度不断提高.为遵循这个原则,我们在分层抽样中所采取第一种方法是,按比例缩小来确定样本单位数结构,这是最简单可行的分配方式.但大多数人认为除遵循样本与总体单位数结构一致性外,还必须考虑总体不同层次方差的差异,满足抽样估计量方差的最小化要求.简而言之,就是指在有限资金、时间或其他与每层的样本分配量相关的条件限制下,分配每层的样本量,使估计量方差最小.这就是本文要研究的样本量最优化分配问题.     

连续性抽样调查中的样本轮换研究

 内容摘要：本文首先介?绍了样本轮换研究问题提出的背景和国内外研究现状。接着介绍了分层抽样下样本轮换的理论模型。包括分层抽样下样本轮换的估计量公式和最优样本轮换率的确定方法。再接着利用前面介绍的理论知识,结合上海市城镇住房空置率抽样调查数据进行实证分析。由于该抽样调查采取的是分层抽样,因此相应地用分层抽样下的样本轮换研究。先根据该抽样调查本身的特点和社会经济活动的规律确定样本轮换时间间隔为1年。再分别计算出各层的最优样本轮换率和总体的样本轮换率。最后分别对三层子总体样本轮换的效果进行分析,分析发现各层经过样本轮换以后的精度比不进行样本轮换或进行完全样本轮换的精度有了明显的提高,轮换效果显著。     

基于“三新”企业分层抽样单元权重动态调整的估计方法

对“三新”企业进行抽样调查是及时掌握和监测“三新”经济发展的重要手段。考虑到这一类调查总体单元变动比较迅速,抽样框信息变动大,无法及时覆盖总体的最新特征,依此抽样框得到的样本数据结构与总体的分布结构差异较大,样本的代表性较低,会对总体数量特征的有效估计产生影响。因此,基于调查总体单元的变动特征,把抽样框中的单元划分为保留单元和转移单元,在此基础上,依据样本单位分层结构的变动,设计了基于“三新”企业分层抽样单元权重动态调整的估计方法。首先,通过事后分层方法挖掘出不同层的单位特征,并预测抽样框各层容量;其次,依据层规模的变动预测对目标变量估计量的权重进行修正;最后,通过自我加权设计构造出总体动态变动后数量特征的复合估计量,并对其进行优良性讨论。在对“三新”企业的模拟数据进行多次重复抽样实验中,相比于固定抽样框下的传统方法,基于分层抽样单元权重动态调整的估计方法具有更高的抽样效率,构造的关于总体数量特征的估计量具有无偏性和有效性。     

双重分层抽样中的校正估计

校正估计法已被大量运用于抽样调查中,它利用辅助信息构造的校正权重提高了对总体总值（或均值）的估计精度。本文提出了分层抽样中的校正组合比率估计量,并推广到分层双重抽样中。同时给出新估计量的近似方差表达式。最后利用计算机随机模拟验证较正估计量对估计精度的改进。     

怎样确定子总体--有关规模以下工业抽样调查的思考

分层抽样是经常使用的一种抽样技 术。采用分层抽时,总体被分为同质但又不相互重叠的若干部分,这些部分被称为子总体或层。 划分子总体的动机大致可分为主动的和被动的两种。所谓主动,又常出于两种考虑:一是为了提高抽样效率,即对于同一个调查总体和同样的调查精度要求,采用不同的抽样方法和估计量所需要的样本量会有很大的差别,样本星小的为抽样效率高,反之,则为抽样效     

对分层抽样设计的改进

 在社会经济研究中,由于实际条件的限制,往往采用抽样调查的方法获得的现象总体的信息,当总体内部差异比较大时,应首先对总体个单位按有关指标加以分层,然后再从各层中按随机原则抽选一定单位构成样本。分层可以大大提高抽样推断的精度,降低工作量和成本,所以实际工作中分层抽样得到了广泛的应用。 样本分配是分层抽样研究的一个重要方面。影响样本分配的因素主要有：各层方差、各层样本单位数、调查成本等,其中调查成本是与实际工作有密切影响的因素。当存在多个项目场合中调查成本与调查精度之间的函数关系,为实际工作中的多目标决策提供思路。     

Multiobjective Stochastic Multivariate Stratified Sampling in Presence of Nonresponse

The case of nonresponse in multivariate stratified sampling survey was first introduced by Hansen and Hurwitz in 1946 considering the sampling variances and costs to be deterministic. However, in real life situations sampling variance and cost are often random (stochastic) and have probability distributions. In this article, we have formulated the multivariate stratified sampling in the presence of nonresponse with random sampling variances and costs as a multiobjective stochastic programming problem. Here, the sampling variance and costs are considered random and converted into a deterministic NLPP by using chance constraint and modified E-model. A solution procedure using three different approaches are adopted viz. goal programming, fuzzy programming, and D₁ distance method to obtain the compromise allocation for the formulated problem. An empirical study has also been provided to illustrate the computational details.     

A note on stratification and gain in precision in estimating diversity from large samples

Several indices of entropy have been suggested in the literature as weighted diversity measures of a population with respect to a classification process. Among them, Shannon's entropy and Havrda -Charvát's non-additive entropies of order a, have been exhaustively used.

When the population is finite but too large to be censused, the diversity with respect to a given classification process must be estimated from a sample.

In this note, on the basis of an asymptotic study of the sample indices in the stratified random sampling, we are going to confirm that when we deal with large samples one can guarantee a gain in precision from stratified random over simple random sampling. This gain becomes considerable when the ‘inaccuracy" (as intended by Kerridge and Rathie and Kannapan) between the frequency vector in each stratum and that in the whole population, varies greatly from stratum to stratum.     

A perspective of composite sampling

Composite samples are formed by physically mixing samples. Usually, composite samples are used to reduce the overall cost associated with analytical procedures that must be performed on each sample, but they can also be used to protect the privacy of individuals.

Composite sampling can reduce the cost of identifying individual cases that have a certain trait, such as those with a rare disease or those exceeding pollution-level standards. Not much is lost by applying this method as long as the trait is relatively rare.

Composite sampling can reduce the cost of estimating the mean of some process. When samples are composited, the ability to estimate the variance is lost. In spite of this, the potential savings are so great that composite samples have been used.

Much of this paper deasl with the variance of estimators based on composite sampling when the porportions of hte original samples comprising the composite sample are actually random. Taking repeated samples and measurements on several composite samples complicates the prodcedure, but allows the estimation of between and within variation as well as measurement error.     

Environmental sampling with a concomitant variable: A comparison between ranked set sampling and stratified simple random sampling

In many environmental sampling situations, the variable of interest is either not easily observable or is too expensive to observe. Under such circumstances, the need arises to observe another variable, related to the variable of interest, so as to estimate the population parameters of interest. We study the performance of two different sampling procedures, i.e. ranked set sampling and stratified simple random sampling, when both stratification and ranking are accomplished on the basis of such a concomitant variable. The relative precision of the two methods is obtained and expressed as a function of population variance, between-stratum and between-rank variation, and the correlation coefficient between the variable of interest and the concomitant variable. The relative precision is computed for several important families of distributions that occur frequently in environmental and ecological work. Under equal allocation of sampling units, stratified simple random sampling is found to perform better than ranked set sampling, when the costs incurred to obtain sample measurements are ignored. When optimum allocation is considered for both methods, ranked set sampling performs better than stratified simple random sampling, when the concomitant variable is not highly correlated with the variable of interest. Furthermore, when the costs of sampling and the costs of measurement are incorporated into the assessment of the relative precision, the ranked set sampling is seen to be more efficient than stratified simple random sampling, particularly when the cost of stratification is high compared with that of ranking. This is generally the case in practice.     

Environmental sampling with a concomitant variable: a comparison between ranked set sampling and stratified simple random sampling

In many environmental sampling situations, the variable of interest is either not easily observable or is too expensive to observe. Under such circumstances, the need arises to observe another variable, related to the variable of interest, so as to estimate the population parameters of interest. We study the performance of two different sampling procedures, i.e. ranked set sampling and stratified simple random sampling, when both stratification and ranking are accomplished on the basis of such a concomitant variable. The relative precision of the two methods is obtained and expressed as a function of population variance, between-stratum and between-rank variation, and the correlation coefficient between the variable of interest and the concomitant variable. The relative precision is computed for several important families of distributions that occur frequently in environmental and ecological work. Under equal allocation of sampling units, stratified simple random sampling is found to perform better than ranked set sampling, when the costs incurred to obtain sample measurements are ignored. When optimum allocation is considered for both methods, ranked set sampling performs better than stratified simple random sampling, when the concomitant variable is not highly correlated with the variable of interest. Furthermore, when the costs of sampling and the costs of measurement are incorporated into the assessment of the relative precision, the ranked set sampling is seen to be more efficient than stratified simple random sampling, particularly when the cost of stratification is high compared with that of ranking. This is generally the case in practice.     

Estimation of Finite Population Mean in Stratified Random Sampling with Two Auxiliary Variables under Double Sampling Design

In this article, a chain ratio-product type exponential estimator is proposed for estimating finite population mean in stratified random sampling with two auxiliary variables under double sampling design. Theoretical and empirical results show that the proposed estimator is more efficient than the existing estimators, i.e., usual stratified random sample mean estimator, Chand (1975) chain ratio estimator, Choudhary and Singh (2012) estimator, chain ratio-product-type estimator, Sahoo et al. (1993) difference type estimator, and Kiregyera (1984) regression-type estimator. Two data sets are used to illustrate the performances of different estimators.     

Multistage Sampling Designs and Estimating Equations

In some applications it is cost efficient to sample data in two or more stages. In the first stage a simple random sample is drawn and then stratified according to some easily measured attribute. In each subsequent stage a random subset of previously selected units is sampled for more detailed and costly observation, with a unit's sampling probability determined by its attributes as observed in the previous stages. This paper describes multistage sampling designs and estimating equations based on the resulting data. Maximum likelihood estimates (MLEs) and their asymptotic variances are given for designs using parametric models. Horvitz–Thompson estimates are introduced as alternatives to MLEs, their asymptotic distributions are derived and their strengths and weaknesses are evaluated. The designs and the estimates are illustrated with data on corn production.     

Pseudo‐empirical likelihood ratio confidence intervals for complex surveys

The authors show how an adjusted pseudo‐empirical likelihood ratio statistic that is asymptotically distributed as a chi‐square random variable can be used to construct confidence intervals for a finite population mean or a finite population distribution function from complex survey samples. They consider both non‐stratified and stratified sampling designs, with or without auxiliary information. They examine the behaviour of estimates of the mean and the distribution function at specific points using simulations calling on the Rao‐Sampford method of unequal probability sampling without replacement. They conclude that the pseudo‐empirical likelihood ratio confidence intervals are superior to those based on the normal approximation, whether in terms of coverage probability, tail error rates or average length of the intervals.     

Analysis of categorical data obtained by stratified random sampling

Analysis of categorical data by linear models is extended to data obtained by stratified random sampling. It is shown that, asymptotically, proportional allocation reduces the variances of estimators from those obtained hy simple random sampling. The difference between the asymptotic covariance matrices of estimated parameters obtained by simple random sampling and stratified random sampling with proportional allocation is shown to be positive definite vinder fairly non-restrictive conditions, when an asymptotically efficient method of estimation is used. Data from a major community study of mental health are used to illustrate application of the technique.     

Designing stratified sampling in economic and business surveys

In most economic and business surveys, the target variables (e.g. turnover of enterprises, income of households, etc.) commonly resemble skewed distributions with many small and few large units. In such surveys, if a stratified sampling technique is used as a method of sampling and estimation, the convenient way of stratification such as the use of demographical variables (e.g. gender, socioeconomic class, geographical region, religion, ethnicity, etc.) or other natural criteria, which is widely practiced in economic surveys, may fail to form homogeneous strata and is not much useful in order to increase the precision of the estimates of variables of interest. In this paper, a stratified sampling design for economic surveys based on auxiliary information has been developed, which can be used for constructing optimum stratification and determining optimum sample allocation to maximize the precision in estimate.