不等概率抽样若干问题探讨

随着抽样调查在我国应用领域的不断扩展,不等概率抽样方法的应用也将越来越普遍。本文拟就其有关问题作一探讨。一、不等概率抽样的估计量及其方差不等概率抽样是指当总体中的个体有大小差异、而所要调查的标志又与其有密切的正相关关系时,按个体大小赋予不同的被抽中概...     

不等概抽样的应用

不等概抽样的应用江西财经管理干部学院袁晋华一、不等概抽样不等概抽样是指在抽取样本单位时每一单位被抽中的概率不完全相等。例如，设总体单位为Ｎ，现从中抽取几个单位组成一个样本，第一个单位被抽中的概率为，第二个单位被抽中的概率为，……，第Ｎ个单位被抽中的概...     

MPPS抽样下Hansen-Hurwitz估计量的扩展

一、问题的提出一般来说 ,在抽样调查中 ,我们会尽量利用已知的辅助信息来提高估计的精度。下面考虑一个包含N个单元的有限总体 ,设y表示我们要研究的变量 ,x是一个已知而且是正的辅助变量 ,且它与变量y高度相关 ,yi 和xi 分别表示第i个单元的研究变量值和辅助变量值 (其中i =1,… ,N)。这样在抽样设计阶段 ,我们就可以充分利用辅助变量x。比如说 ,在放回抽样中 ,我们以pi 作为第i个总体单元被抽中的概率 (其中i =1,… ,N) ,而pi 的大小取决于已知的辅助变量值xi,即满足pi >0 ,∑Ni =1pi =1。在这样一种放回的不等概率抽样中 ,如果让每个…     

辅助信息在二重抽样中的应用

一、问题的提出在抽样理论中,我们往往会利用研究总体的某些辅助信息来提高估计的精度。比如,在抽样设计阶段,可以利用辅助信息进行不等概率抽样或者分层抽样;在估计阶段,可以利用辅助信息进行比率估计和回归估计。但是,在有些情况下,这些关于总体的辅助信息在抽样之前并不知道     

抽样调查中样本容量的确定方法

确定样本容量是抽样调查中重要的环节,直接关系到抽样估计的精确度及调查的成本和效益。单位标志变异程度、抽样极限误差、抽样推断的可靠度、抽样类型和方法等影响到样本容量的确定。文章提出,样本容量的确定可以根据由抽样误差、抽样极限误差和概率度推算出来的公式计算,也可以根据经验法则来确定。     

样本容量愈大抽样误差愈小吗?

一般地讲,影响抽样误差大小的因素主要有三种:第一,总体标志的变异程度;第二,样本容量的大小;第三,抽样的组织形式与抽样方法.而目前许多的《社会经济统计学原理》教科书上,在对第二种影响因素进行分析时,往往后面总要写上这样的话:当样本单位数(n)扩大到接近总体或等于总体单位数(N)时,抽样调查就接近于全面调查或就是全面调查,因而此时的抽样误差(μ_x或μ_p)就缩小到几乎为零或等于零.     

一种处理不可忽略抽样机制下的小域估计的新方法

在小域估计中,由于抽样过程的复杂性以及不等概抽样的广泛使用,往往会出现样本域的抽样过程与域均值相关以及域内样本单元的选择过程与目标变量有关的情况,即不可忽略的抽样机制。文章介绍了一种解决处理不可忽略抽样机制下的小域估计问题的新方法;并通过一个模拟案例说明了这种方法可以得到样本域和非样本域的近似无偏的域估计。     

多目标抽样的区间估计方法

实践中经常会碰到一些多目标抽样的问题,由于总体单位在各个目标上的差异往往很大,给抽样调查的设计、目标量的估计、样本容量的确定以及抽样误差的控制等方面带来了困难,因而如何兼顾各个目标的要求是多目标抽样研究的难题之一。笔者试提出一种多目标抽样的区间估计方法,希望能够从一个总体的角度对总体参数的置信区间进行测量,从而避免各个目标     

按与单位大小成比例的概率抽样

大多数的抽样调查都是建立在对总体进行等概随机抽样的基础之上的.即当抽样框建立之后,抽样框中的每一个单位都有同样的概率被抽中.这种抽样方法并不适用于每一种抽样框.若不将所要调查的问题与抽样框中单位加以综合考虑,而都采用简单随机抽样,甚至其它的一些复杂随机抽样的方法来进行推断,都将造成样本的偏斜.例如,某省旅游部门想了解接待国外旅游者的能力,一个最希望知道的信息是宾馆房间数,若所选择的抽样框是该省各大、中、小城市的目录表,一个地区的中小城市总是比大城市多,若用简单随机抽样,则样本中的中、小城市就很多,而中、小城市无论是宾馆数,还是宾馆的规模与大城市都有较大的差异,这就造成了样本的偏斜.同样,若某地区的卫生部门想了解该     

类型抽样方法的实际应用

类型抽样也称分层抽样或分类抽样,是抽样调查中常用的方法。一般认为,用类型抽样可缩小抽样误差,提高抽样指标的代表性,从而提高抽样推算的精度。一、类型抽样的定义类型抽样是将总体中所有单位按一定的属性或特征分成不相重迭的若干类型组,然后在每个类型组中进行随机抽样或机械抽样。根据总体单位标志差异越小,抽样误差会越小这一原理,运用分组法可以把样本单位在各类别之间的分布均匀,使组内标志差异缩小,从而提高抽样指标的代表性。如商业零售企业规模不同,零售额差异极大,通过分类划分     

Optimality of Equal vs. Unequal Cluster Sizes in Multilevel Intervention Studies: A Monte Carlo Study for Small Sample Sizes

Optimality of equal versus unequal cluster sizes in the context of multilevel intervention studies is examined. A Monte Carlo study is done to examine to what degree asymptotic results on the optimality hold for realistic sample sizes and for different estimation methods. The relative D-criterion, comparing equal versus unequal cluster sizes, almost always exceeded 85%, implying that loss of information due to unequal cluster sizes can be compensated for by increasing the number of clusters by 18%. The simulation results are in line with asymptotic results, showing that, for realistic sample sizes and various estimation methods, the asymptotic results can be used in planning multilevel intervention studies.     

General orthogonal designs for parameter estimation of ANOVA models under weighted sum-to-zero constraints

ABSTRACT

Traditional studies on optimal designs for ANOVA parameter estimation are based on the framework of equal probabilities of appearance for each factor's levels. However, this premise does not hold in a variety of experimental problems, and it is of theoretical and practical interest to investigate optimal designs for parameters with unequal appearing odds. In this paper, we propose a general orthogonal design via matrix image, in which all columns’ matrix images are orthogonal with each other. Our main results show that such designs have A- and E-optimalities on the estimation of ANOVA parameters which have unequal appearing odds. In addition, we develop two simple methods to construct the proposed designs. The optimality of the design is also validated by a simulation study.     

New monte carlo results on the robustness of the anova f,w and f statistics

Because the usual F test for equal means is not robust to unequal variances, Brown and Forsythe (1974a) suggest replacing F with the statistics F or W which are based on the Satterthwaite and Welch adjusted degrees of freedom procedures. This paper reports practical situations where both F and W give * unsatisfactory results. In particular, both F and W may not provide adequate control over Type I errors. Moreover, for equal variances, but unequal sample sizes, W should be avoided in favor of F (or F ), but for equal sample sizes, and possibly unequal variances, W was the only satisfactory statistic. New results on power are included as well. The paper also considers the effect of using F or W only after a significant test for equal variances has been obtained, and new results on the robustness of the F test are described. It is found that even for equal sample sizes as large as 50 per treatment group, there are practical situations where the F test does not provide adequately control over the probability of a Type I error.     

The precision of regression-type estimator for incremental cost–effectiveness ratio

The estimation of incremental cost–effectiveness ratio (ICER) has received increasing attention recently. It is expressed in terms of the ratio of the change in costs of a therapeutic intervention to the change in the effects of the intervention. Despite the intuitive interpretation of ICER as an additional cost per additional benefit unit, it is a challenge to estimate the distribution of a ratio of two stochastically dependent distributions. A vast literature regarding the statistical methods of ICER has developed in the past two decades, but none of these methods provide an unbiased estimator. Here, to obtain the unbiased estimator of the cost–effectiveness ratio (CER), the zero intercept of the bivariate normal regression is assumed. In equal sample sizes, the Iman–Conover algorithm is applied to construct the desired variance–covariance matrix of two random bivariate samples, and the estimation then follows the same approach as CER to obtain the unbiased estimator of ICER. The bootstrapping method with the Iman–Conover algorithm is employed for unequal sample sizes. Simulation experiments are conducted to evaluate the proposed method. The regression-type estimator performs overwhelmingly better than the sample mean estimator in terms of mean squared error in all cases.     

Selecting the better binomial population under a budget constraint

The problem of optimal non-sequential allocation of observations for the selection of the better binomial population is considered in the case of fixed sampling costs and budget. With the appropriate choice of selection rule it is shown that a 70% reduction in the probability of incorrect selection is possible by using an unequal rather than equal allocation. Simple formulae are given for the appropriate selection rule and unequal allocation in large samples.     

Classifying weibull populations with respect to a control

This paper is concerned with classifying k Weibull populations by their reliabilities with respect to a control population. He have proposed procedures which can be used for maximum likelihood estimators or simplified linear estimators of the parameters. Estimators are based on type II censored data. The cases considered include unknown shape parameters being equal or unequal. In selected cases, the constants needed for the procedures are tabulated using Monte Carlo methods.     

A step-down heteroscedastic multiple comparison procedure

All-pairs power in a one-way ANOVA is the probability of detecting all true differences between pairs of means. Ramsey (1978) found that for normal distributions having equal variances, step-down multiple comparison procedures can have substantially more all-pairs power than single-step procedures, such as Tukey’s HSD, when equal sample sizes are randomly sampled from each group. This paper suggests a step-down procedure for the case of unequal variances and compares it to Dunnett's T3 technique. The new procedure is similar in spirit to one of the heteroscedastic procedures described by Hochberg and Tamhane (1987), but it has certain advantages that are discussed in the paper. Included are results on unequal sample sizes.     

Fast,closed-form,and efficient estimators for hierarchical models with AR(1) covariance and unequal cluster sizes

This article is concerned with statistically and computationally efficient estimation in a hierarchical data setting with unequal cluster sizes and an AR(1) covariance structure. Maximum likelihood estimation for AR(1) requires numerical iteration when cluster sizes are unequal. A near optimal non-iterative procedure is proposed. Pseudo-likelihood and split-sample methods are used, resulting in computing weights to combine cluster size specific parameter estimates. Results show that the method is statistically nearly as efficient as maximum likelihood, but shows great savings in computation time.     

A design-based randomized response procedure for the estimation of population proportion and sensitivity level

A general design-based approach to randomized response surveys is proposed. The method is tailored for the joint estimation of the proportion of individuals in the population bearing a sensitive attribute and the proportion of individuals in the sensitive group declaring truthfully their status. The proposal is specialized to the case of simple random sampling without replacement, unequal probability sampling without replacement and stratified sampling.     

Interval estimation of the largest reliability of k weibull populations

A procedure is given for obtaining a random width confidence interval for the largest reliability of k Weibull populations. The procedure does not identify the populations for which the reliability would be a maximum. The maximum likelihood estimators or the simplified linear estimators of the reliability based on type II censored data are used. The cases considered include unknown shape parameters being equal or unequal. Simultaneous confidence intervals for the k reliabilities are also obtained. Tables for the lower and upper limits in selected cases are constructed using Monte Carlo methods.