多阶连续抽样设计下广义加权回归估计方法研究

在抽样调查领域中,关于抽样方案设计的研究应用较为充分和完整,但关于抽样估计的研究应用却较为缺乏和滞后。本文首先总结了国外相关研究成果,研究了基于广义加权回归的抽样估计方法,同时证明其满足渐近设计无偏和最小化渐近期望方差的理论条件。同时,本文以各类常见的抽样设计为基础,通过模型组和模型水平将现有的超总体回归模型进行扩展,基于复杂的多阶连续抽样调查,建立各种类型的超总体回归模型进行模型辅助的广义加权回归抽样估计,给出了具体的回归估计步骤和结果,最终形成一套关于广义加权回归抽样估计的理论方法体系,为抽样估计方法在我国政府统计部门中的有效应用奠定理论基础。     

多阶等距抽样下总体总值估计量的方差估计

本文给出了多阶抽样下构造总体总值估计量的方差估计量的一种方法．由此，可以得到多阶等距抽样下总体总值估计量的方差估计．     

基于超总体伪设计与组合样本的候选者数据库网络调查的推断研究

候选者数据库网络调查的推断问题是网络调查发展中迫切需要解决的问题.基于此,提出基于超总体伪设计与组合样本的非概率抽样推断方法:对网络候选者数据库的调查样本建立超总体模型来构造伪权数,并根据网络候选者数据库的调查样本和概率样本的组合样本计算总体均值的估计,最后根据超总体模型的方差估计理论推导出目标总体均值估计的方差估计式,同时采用Bootstrap与Jackknife方法来估计总体均值估计的方差,并比较不同方差估计方法的效果.研究结果表明:基于超总体伪设计与组合样本的总体均值估计效率高于仅使用概率样本的估计和仅使用网络候选者数据库的调查样本加权的估计,估计效果较好;方差估计方面,采用VM1、VM2与VM3方法计算的方差估计相比而言更好.     

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.     

等距抽样总体指标估计值的优良判定

等距抽样是实践中常用的一种抽样方法，它是事先将全区及总体各单位按某一标志排列，然后依固定顺序和间隔来抽选调查单位，以样本来推断总体．在实践中常用“随机确定起点，对称等距抽样”、“半距起点，顺序等距抽样”的方法．近几年，学术界对样本指标的推断研究的较多，但对这一抽样方法总体指标的估计却很少问究，致使实践中的估计方法较单一，抽样效果难以提高。本文想就标志等距抽样总体指标值的估计进行分析．为实际中的抽样技术提供理论上的数学依据。     

有限总体指标值的线性函数的可容许估计

基于超总体模型的观点讨论容许性问题。在期望均方误差准则下获得了有限总体指标值的线性函数之线性估计在线性估计类以及全体估计类中为可容许的充要条件。     

抽样调查中多个指标值的同时估计

本文在ＥＶ（Ｅｒｏｒ ｉｎ Ｖａｒｉａｂｌｅｓ）超总体模型下讨论有限总体两个指标值的同时估计问题，证明了样本均值作为整体均值的估计在均方差阵最小的意义下是最优的．     

集团抽样不等概方法的均值估计及其性质

在集团抽样调查中，［１］和［２］给出了一般抽样方法及均值估计和它性质的论述，但未考虑各集团在总体中的地位对估计结果的影响．本文给出了集团抽样的不等概方法和均值的无偏估计，同时也给出了这种估计的方差及方差的无偏估计．     

PPS适应性整群抽样下估计量的研究

在群规模存在差异时,最有效的抽样方法是PPS整群抽样;在单元存在聚集性且总体信息不明确时,使用PPS适应性整群抽样是最有效的.利用PPS适应性整群抽样设计中的样本外推机制产生的样本信息,对HH和HT估计进行调整,提出修正的HH和HT估计,并对估计量的性质进行了研究.     

分层整群抽样的Warner模型RRT技术及其对大学生婚前性行为调查中的应用

本文的目的为敏感性问题提供科学的较复杂抽样调查方法及其统计量的计算公式。使用Cochran W.G.的抽样理论、随机应答技术的Warner模型、全概率公式、方差的基本性质等理论与方法,推导出二分类敏感问题随机应答技术Warner模型在整群抽样、分层整群抽样下总体比例的估计量及其估计方差的计算公式,并在苏州大学学生婚前性行为的调查中取得了信度较高的成功应用效果。     

Local asymptotic normality of sampling experiments

Summary Following Hájek's and Madow's asymptotic approach to classical survey sampling, a framework for the asymptotic analysis of superpopulation models is proposed. Within this framework weak limit theorems for sequences of experiments obtained by Poisson sampling and Rejective sampling are derived. In particular, it is shown that the sampling experiments are locally asymptotically normal in LeCam's sense, if the underlying superpopulation model is an L ²-generated regression experiment. This result can e.g. be used to produce Horvitz-Thompson-type estimators which are asymptotically efficient median-unbiased estimates of certain functionals of the regression function.     

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??How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

Research on Inference of Candidate Database Web Surveys Based on Superpopulation Pseudo Design and the Combined Sample

How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

Model-based design in small area estimation

In this paper, we address the problem of an efficient estimation strategy when solving real survey sampling problems. We consider the panel data model with random effects as a superpopulation model. We investigate the performance of model-assisted estimators under model-based sample designs in a simulation experiment based on the real data (Lithuanian survey on short-term statistics on service) taken as a true population. Here the model-based sampling refers to a sample design constructed using the model and information about the behavior of the model-assisted estimator on available auxiliary data.     

Comparison of variance estimators for the ratio estimator based on small sample

1. Introduction and Main ResultsSuppose the population of interest consists of N distinct units labelled by 1,' f N.Associated with unit i are two values K and Xi, with Xi > 0 (i = 1,' t N). Denote thepopulation means of K and X, by Y and X respectively. To estimate Y, it is customaryto select a simple raPdom sample of size n and to use the ratio estimatNn = RX if Xis available, where R = y/x is an estimator for population ratio R = Y/X, y and x arerespectively the 8ample mean8 of…     

任意秩有限总体中的简单投影预测

本文得到了任意秩有限总体中的简单投影预测为最优预测的充要条件 ,并研究了简单投影预测关于协方差矩阵的稳健性     

Admissible estimation of linear functions of characteristic values of a finite population

The problem on admissibility of estimators is considered based on the point of view of the superpopulation model. The necessary and sufficient conditions for linear estimators of an arbitrary linear function of characteristic values of a finite population to be admissible in the class of linear or all estimators are obtained respectively. Project supported by the National Natural Science Foundation of China.     

Statistical analysis of hierarchical stochastic models: Examples and approaches

This paper introduces and illustrates the concept of hierarchical or random parameter stochastic process models. These models arise when members of a population each generate a stochastic process governed by certain parameters and the values of the parameters may be viewed as single realizations of random variables. The paper treats the estimation of the individual parameter values and the parameters of the superpopulation distribution. Examples from system reliability, pharmacokinetic compartment models, and criminal careers are introduced; a reliability (Poisson process-exponential interval) process is examined in greater detail. An explicit, approximate, robust estimator of individual (log) failure rates is presented for the case of a long-tailed (Studentt) superpopulation. This estimator exhibits desirable limited shrinkage properties, refusing to borrow unjustified strength. Numerical properties of such estimators are described more fully elsewhere.     

Estimation de l'évolution d'un total en présence d'information auxiliaire : une approche par splines de régression

We build an estimator for the evolution of a finite population total between two periods of time when auxiliary information is available. A superpopulation model is introduced in order to explain the relationship between the study and the auxiliary variables. The regression functions are estimated by regression splines and Horvitz–Thompson technique. Finally, an estimator for the evolution is derived and proved to be asymptotically unbiased and consistent and we compute a design-based variance formula. To cite this article: C. Goga, C. R. Acad. Sci. Paris, Ser. I 339 (2004).