二维平衡单水平轮换设计及其广义组合估计方法研究

针对国内外现行单水平轮换调查存在的一系列问题,本文提出二维平衡单水平轮换模式设计及其广义组合估计方法。在这套设计方法中,将轮换偏差和两类相关关系引入到广义组合估计量公式中,提高了估计量的准确性,同时在连续性的多目标调查下还应用最优化方法确定一套最优权重系数,使得抽样调查的整体精度达到最高,同时又能够调整权重,满足各类目标量精度高低的要求。这套系统化、理论化的设计方法将为我国今后更好地开展各类单水平轮换调查提供理论指导。     

模型辅助条件下广义最优回归抽样估计方法研究

在抽样估计中,当超总体模型为非线性形式时,广义回归估计量和最优估计量的估计效果均有待提高,而非参数回归估计量虽然能在一定程度上提高估计精度,但需要获得全部总体单位的辅助变量值,这在实际调查中往往难以满足。本文基于传统的广义回归估计量和最优估计量,借鉴非参数回归中局部多项式的估计思想,对原始辅助变量信息进行扩展,得到原始辅助变量多次方形式的新辅助变量,进而研究提出广义最优回归估计量。该估计量可以克服广义回归估计量、最优估计量和非参数回归估计量的缺陷,并证明其满足渐近无偏性和一致性。在不同超总体模型下,通过数值模拟方法比较了各类回归抽样估计方法的估计效果,模拟结果显示:在线性模型下,除了π估计量的精度较差,其余各类估计量的估计精度基本相同;但在非线性模型下,最优估计量和广义回归估计量的估计精度明显下降,而广义最优回归估计量和非参数的局部多项式回归估计量的估计精度都较好。     

基于广义回归估计的校准加权设计效应模型研究

校准是最常用的加权调整方法,然而传统加权调整设计效应模型只考虑有差异权数导致的精度损失,忽略使用辅助信息后的精度改进,因此应用于设计效应计算时存在一定的缺陷。本文在Spencer模型的基础上进行拓展,引入反映辅助变量和调查变量相关关系的广义回归估计量,构建了校准加权设计效应的一般模型。数值分析结果显示,校准加权设计效应模型的效果优于传统加权调整设计效应模型;尤其在调查变量与辅助变量高度相关的情形下,校准加权设计效应模型能够准确地估计出不等概率抽样设计和校准调整的综合效率。     

基于分层抽样的校准方法分别比率-乘积估计研究

比率估计在抽样估计阶段利用辅助信息,提高了估计量的估计精度,是抽样调查中一类较为常用的估计方法,但现有的一些比率估计方法均具有各自的最优条件,这在一定程度上影响了它们在实际调查中的应用。为了解决比率估计的最优限制问题,本文引入了校准估计方法,并基于分层抽样研究了总体均值的校准方法分别比率-乘积估计量。在大样本情况下,本文推导了新估计量的估计偏差和均方误差,说明新估计量具有渐近无偏性,并在估计量均方误差最小时,得到了总体参数的渐近最优估计量和渐近最优估计量的方差。在模拟研究中,根据比率估计量的最优条件是否满足,本文生成了两种不同的总体,对比分析了新估计量和现有比率估计量的估计效果,结果表明在两种不同的情况下,新估计量的估计效果均优于现有估计量的估计效果。最后,本文利用一个实际例子,验证了新估计量的有效性和实用性。     

双无回答层抽样的三重抽样比率估计量

无回答在抽样调查中经常出现,无回答层再抽样是解决无回答的常用方法.当辅助变量总体均值未知时,本文讨论了双无回答层抽样的三重抽样方法,给出了三重抽样的分层汉森-赫维茨估计量和比率估计量,以及它们的方差和估计方差.给出满足事前给定总调查费用约束的三重抽样过程的最优设计参数,以及比率估计量的方差估计.给定总调查成本,三重抽样的分层汉森—赫维茨估计量与比率估计量进行模拟比较,演示比率估计量的优良性.     

基于辅助信息的分层排序集抽样及调查费用分析北大核心

辅助信息在改进和完善抽样设计、提高抽样估计精度和节省抽样费用等方面具有重要作用,鉴于此,基于分层排序集样本建立了总体均值的比率估计量,同时考虑估计精度和调查费用两个方面,证明了抽样方案的优良性.最后,通过实例进一步分析,结果表明,在给定的估计精度下,分层排序集抽样方法可以有效降低抽样调查费用.     

基于辅助信息的分层排序集抽样及调查费用分析

辅助信息在改进和完善抽样设计、提高抽样估计精度和节省抽样费用等方面具有重要作用,鉴于此,基于分层排序集样本建立了总体均值的比率估计量,同时考虑估计精度和调查费用两个方面,证明了抽样方案的优良性.最后,通过实例进一步分析,结果表明,在给定的估计精度下,分层排序集抽样方法可以有效降低抽样调查费用.     

基于双系统估计量的中国非普查年人口总数估计

针对当前中国非普查年人口总数估计方法的不足,本文提出利用人口抽样调查及其事后质量评估调查数据,构造基于捕获再捕获模型的非普查年人口总数双系统估计量。首先,介绍双系统估计量的构造及其估计方法。其次,研究如何利用刀切法构建双系统估计量的方差估计。最后,通过一组模拟数据演示非普查年人口总数双系统估计量及其方差估计的构造过程。本文的研究能显著提高中国非普查年人口总数估计的准确性和可靠性,并对未来中国人口抽样调查的方案设计提供理论指导。     

序贯调整估计量——不完全事后分层估计的新方法

在使用多个分类变量对样本进行交叉事后分层时,边缘总值已知、格子总值未知的不完全事后分层问题是估计时经常面临的情况。序贯调整估计量是本论文提出的解决这一问题的新方法。在详细介绍了序贯调整估计程序后,论文用随机模拟的方法研究了该估计量的数学性质,并将其与经典的不完全事后分层估计量做了比较。     

对不完全事后分层的估计

事后分层估计量是抽样调查中经常用到的一种估计方法。在使用多个分类变量对样本进行交叉事后分层时,边缘总值已知、格子总值未知的不完全事后分层问题是估计时又常面临的情况。本论文将对这一情况进行系统的总结,给出两个经典的估计量:搜索比率估计量和广义搜索比率估计量。     

利用分层抽样数据中完全辅助信息的模型校正方法

In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator(or GREG).     

An Information-theoretic Approach to the Effective Usage of Auxiliary Information from Survey Data

In this paper, we propose an information-theoretic approach to the effective usage of auxiliary information from survey data, which is suitable for both simple and complex survey data. Our estimator under simple random sampling without replacement will be consistent and asymptotically normal. We show that the resulting estimates have smaller asymptotic variances than the usual estimates which do not use auxiliary information. For more complex survey designs, the resulting estimator is in essence asymptotically equivalent to a pseudo empirical likelihood estimator. Results of a limited simulation study show that the proposed estimators perform well among a number of competitors.     

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.     

Ratio methods to the mean estimation with known quantiles

We address the problem of estimating the finite population mean in survey sampling, by exploiting any available auxiliary information in order to increase the precision of classical estimators. The idea is to use any population quantiles of the available auxiliary variables which are known in many real situation from census, administrative files, etc. This is achieved using these known quantities in the construction of the estimators, by modifying the usual ratio estimation methods and afterwards defining a general class of exponentiation ratio estimators. The advantages of the proposed estimators are demonstrated using theoretical asymptotic tools and through a simulation study.     

基于平衡样本的校准估计研究--以规模以下工业企业测算为例

为解决规模以下工业企业调查中存在的样本代表性不足的问题,提出基于平衡样本的校准估计方法,并得出相应的估计量和估计量方差。该方法在抽样设计阶段采用了平衡抽样设计,在估计阶段采用了校准估计方法,较大限度地使用了辅助信息;通过数据分析得出基于平衡样本的校准估计方法要优于基于平衡抽样的HT估计方法。同时,为满足平衡变量间线性无关的假定,提出使用主成分分析、切片逆回归和切片平均方差估计三种方法对相关的平衡变量进行处理的思路。该方法对我国规模以下工业企业调查的完善具有理论与实践的双重意义,可适当的推广至我国政府统计的其他调查中。     

回归系数的广义根方估计及其模拟

文献[1,2]中提出了回归系数的根方估计~(k),当回归自变量间存在复共线关系时,~(k)较回归系数的最小二乘估计有所改善,本文将根方估计作一拓广,得出了回归系数的广义根方估计~(K),其中K为对角阵,文中证明了广义根方估计~(K)较~(k)能更有效地改善最小二乘估计,并给出了广义根方估计的显式解,在此基础上,提出了广义根方估计的显式解和一种确定k_i的方法。     

Missing data and auxiliary information in surveys

Summary  This paper proposes estimation methods with auxiliary information when some observations are missing from the sample. These ratio, difference and regression methods are proposed for any sampling design and are compared with other complete case estimators.     

On the Bias of the Generalized Regression Estimator in Survey Sampling

It is well known that the generalized regression (GREG) estimator of the finite population total is asymptotically unbiased. Consequently, bias is negligible when the sample size is large. But the magnitude of the bias is not known, if we are estimating small areas or operating with small samples. Furthermore, beside the sample size, the bias depends on the auxiliary variables, on their relation to the study variable and on the sampling design. In small samples it is important to know sources of the bias and in some cases to use a bias-corrected regression estimator. The aim of the present paper is to derive approximate bias expressions of the GREG estimator under different population models and different sampling designs to study the magnitude of the bias.      

Nonparametric regression function estimation with surrogate data and validation sampling

This paper develops estimation approaches for nonparametric regression analysis with surrogate data and validation sampling when response variables are measured with errors. Without assuming any error model structure between the true responses and the surrogate variables, a regression calibration kernel regression estimate is defined with the help of validation data. The proposed estimator is proved to be asymptotically normal and the convergence rate is also derived. A simulation study is conducted to compare the proposed estimators with the standard Nadaraya-Watson estimators with the true observations in the validation data set and the complete observations, respectively. The Nadaraya-Watson estimator with the complete observations can serve as a gold standard, even though it is practically unachievable because of the measurement errors.