基于平衡样本的最优模型辅助抽样策略

模型辅助方法的思想是基于抽样设计借助于超总体模型获得对总体参数的有效推断.满足辅助变量的HT估计等于总体总量真值的样本被称为平衡样本.对于平衡样本,如果超总体模型的异方差性可以通过辅助变量解释,由此得出最优抽样策略:平衡抽样设计与HT估计结合是最优策略,包含概率正比于模型残差的标准差.     

改进样本代表性的多目标追加平衡设计

本文主要讨论样本代表性的改进和多目标调查两个问题。一,本文提出了一种新的改进样本代表性多目标抽样方法,增加样本量与调整样本结构相结合的方法-追加样本的平衡设计,即通过追加样本,使得补充的样本与原来的样本组合生成新的平衡样本,相对于初始样本,减少样本与总体的结构性偏差。平衡样本是指辅助变量总量的霍维茨汤普森估计量等于总体总量真值。二,平衡样本通过选择与多个目标参数相关的辅助变量,使得一套样本对不同的目标参数而言都具有良好的代表性,进而完成多目标调查。结合2010年第六次人口分县普查数据,通过选择多个目标参数,对追加样本后的平衡样本作事后评估结果表明,追加平衡设计能够有效改进样本结构,使得样本结构与总体结构相近,降低目标估计的误差;同时也说明平衡抽样设计能够实现多目标调查,提高样本的使用效率。     

经济社会调查中的空间平衡抽样设计

在经济社会调查中,总体单元之间的空间相关性普遍存在,对传统抽样设计提出了挑战。针对这一问题,提出了使用经纬度坐标作为空间辅助信息,借助空间平衡抽样算法获取样本的设计思路。该种算法利用总体单元之间的空间距离设计抽样算法更新包含概率,使空间上距离较近的单元倾向于不同时进入样本,从而使样本单元在空间上均匀覆盖。实证研究结果表明,随着样本量连续增加,空间平衡抽样设计的估计量标准差在合理的抽样比范围内总是优于传统抽样设计,能够显著提高估计效率。     

住户调查中代表性样本的一种探索获取方法——平衡抽样设计

住户调查是我国社会经济统计调查体系的重要组成部分,样本代表性直接决定统计数据质量。多阶段抽样中初级单元的方差对估计的影响是主要的,因此本文结合2010年全国第六次人口普查分县数据,采用平衡抽样设计获取初级单元的代表性样本-平衡样本。对代表性样本的事后评估结果表明,样本结构与总体结构吻合,目标估计的误差很小,说明了本文平衡设计的有效性。     

Polya后验方法在有限总体抽样估计中的模拟研究

polya后验方法作为一种无信息贝叶斯估计方法,在有限总体抽样中,通过观测的样本,构造一系列的模拟总体,然后进行统计推断。通过统计模拟研究了polya后验方法估计的一些特点,并和Bootstrap方法进行比较。模拟结果显示:polya后验方法能够很好地估计总体的均值,随着样本量的增大,估计值与真值的差距越来越小。采用polya后验方法构造的置信区间区间长度较小,能够很好地覆盖真值。     

不放回样本追加策略下域的估计

 本文研究了不放回追加策略，包括基本设计和域追加设计都为简单随机抽样、分层随机抽样情形下不放回样本追加时域的估计的问题。根据不同的抽样设计给出单元的一阶及二阶包含概率的具体计算公式，并构造总体总量和域总量的Horvitz—Thompson型估计，然后基于简单随机抽样的不放回追加抽样方案，给出总体单元的前两阶包含概率。及该方案在分层抽样下的推广，在有辅助信息可用时构造域总量的分层联合比估计，并给出其方差和方差估计公式，同时我们给出了模拟结果，从模拟结果可以看出，给出的方差估计是估计量方差的近似无偏估计。     

空间抽样中最优单元尺寸确定方法研究

在依据空间区域抽样框进行抽样设计中,抽样单元尺寸的大小影响着估计精度和调查成本,依据主观经验划分单元尺寸会对抽样精度和成本带来很大影响。基于单元尺寸、调查成本等影响因素,构造考虑空间抽样的交通、设计和调查的成本函数,给出成本约束下总体总量有效估计的最优单元尺寸的确定方法。以陕西省GDP的总量估计为例进行了实证研究,结果表明:在成本约束下,基于最优单元尺寸的抽样框相比于其它尺寸抽样框的样本方差较小,具有较高抽样估计精度。     

一种基于多变量空间非概率抽样方法的设计

文章基于样本均值无偏估计和有效估计的前提下,以行政区域单位划分为抽样框,采用多个辅助指标控制多目标抽样估计的误差,设计了一种多指标空间非概率抽样样本选取方法.并利用陕西省2014年城镇人均可支配收入以及人口增长率两个辅助指标对陕西省107个区县进行了抽样应用,结果显示样本的抽取涵盖了各个不同水平层次的区县,抽样效果良好.     

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.     

抽样调查中基于模型的稳健预测方法

基于模型的推断是抽样技术中推断估计量的一种重要方式。文章研究得出,当比率估计模型或者扩张估计模型偏离总体真实模型时,比率估计和扩张估计往往是有偏的,平衡样本能够消除比率估计和扩张估计的偏倚,使得估计量是偏倚稳健的。     

Rao and Wu's re-scaling bootstrap modified to achieve extended coverages

Horvitz and Thompson's (HT) [1952. A generalization of sampling without replacement from a finite universe. J. Amer. Statist. Assoc. 47, 663–685] well-known unbiased estimator for a finite population total admits an unbiased estimator for its variance as given by [Yates and Grundy, 1953. Selection without replacement from within strata with probability proportional to size. J. Roy. Statist. Soc. B 15, 253–261], provided the parent sampling design involves a constant number of distinct units in every sample to be chosen. If the design, in addition, ensures uniform non-negativity of this variance estimator, Rao and Wu [1988. Resampling inference with complex survey data. J. Amer. Statist. Assoc. 83, 231–241] have given their re-scaling bootstrap technique to construct confidence interval and to estimate mean square error for non-linear functions of finite population totals of several real variables. Horvitz and Thompson's estimators (HTE) are used to estimate the finite population totals. Since they need to equate the bootstrap variance of the bootstrap estimator to the Yates and Grundy's estimator (YGE) for the variance of the HTE in case of a single variable, i.e., in the linear case the YG variance estimator is required to be positive for the sample usually drawn.     

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。     

Improved variance estimation for balanced samples drawn via the cube method

The cube method proposed by Deville and Tillé (2004) enables the selection of balanced samples: that is, samples such that the Horvitz-Thompson estimators of auxiliary variables match the known totals of those variables. As an exact balanced sampling design often does not exist, the cube method generally proceeds in two steps: a “flight phase” in which exact balance is maintained, and a “landing phase” in which the final sample is selected while respecting the balance conditions as closely as possible. Deville and Tillé (2005) derive a variance approximation for balanced sampling that takes account of the flight phase only, whereas the landing phase can prove to add non-negligible variance. This paper uses a martingale difference representation of the cube method to construct an efficient simulation-based method for calculating approximate second-order inclusion probabilities. The approximation enables nearly unbiased variance estimation, where the bias is primarily due to the limited number of simulations. In a Monte Carlo study, the proposed method has significantly less bias than the standard variance estimator, leading to improved confidence interval coverage.     

When does an imperfect sampling frame produce more efficient estimators than a perfect frame?

The issue of when imperfect sampling frames can result in more efficient estimators of population totals than perfect frames is explored. Our analysis is based on an expression we call the difference score. We show how, when properly expanded it provides an illuminating basis for comparing a weighted estimator under an imperfect frame with that of a conventional estimator assuming the frame has been corrected. Specifically, the circumstances (i.e., population and frame characteristics) under which an imperfect frame results in estimates of population totals that are more precise than those from a perfect frame can in many cases be discerned by analytically examining the terms in the expansion of this difference score. In addition, a classification tree methodology was used to further explore circumstances under which imperfect frames result in more precise estimators. The results of this analytical study complement, strengthen, and in many cases explain those discovered in an earlier empirical investigation that lead to recommendations as to when to correct a frame or when to adjust for imperfection using a weighting methodology called the arc weight estimator.     

Recursive computation of inclusion probabilities in ranked-set sampling

We derive recursive algorithms for computing first-order and second-order inclusion probabilities for ranked-set sampling from a finite population. These algorithms make it practical to compute inclusion probabilities even for relatively large sample and population sizes. As an application, we use the inclusion probabilities to examine the performance of Horvitz-Thompson estimators under different varieties of balanced ranked-set sampling. We find that it is only for balanced Level 2 sampling that the Horvitz-Thompson estimator can be relied upon to outperform the simple random sampling mean estimator.     

A calibrated imputation method for secondary data analysis of survey data

In practical survey sampling, missing data are unavoidable due to nonresponse, rejected observations by editing, disclosure control, or outlier suppression. We propose a calibrated imputation approach so that valid point and variance estimates of the population (or domain) totals can be computed by the secondary users using simple complete‐sample formulae. This is especially helpful for variance estimation, which generally require additional information and tools that are unavailable to the secondary users. Our approach is natural for continuous variables, where the estimation may be either based on reweighting or imputation, including possibly their outlier‐robust extensions. We also propose a multivariate procedure to accommodate the estimation of the covariance matrix between estimated population totals, which facilitates variance estimation of the ratios or differences among the estimated totals. We illustrate the proposed approach using simulation data in supplementary materials that are available online.     

Spatially Balanced Sampling of Continuous Populations

When sampling from a continuous population (or distribution), we often want a rather small sample due to some cost attached to processing the sample or to collecting information in the field. Moreover, a probability sample that allows for design‐based statistical inference is often desired. Given these requirements, we want to reduce the sampling variance of the Horvitz–Thompson estimator as much as possible. To achieve this, we introduce different approaches to using the local pivotal method for selecting well‐spread samples from multidimensional continuous populations. The results of a simulation study clearly indicate that we succeed in selecting spatially balanced samples and improve the efficiency of the Horvitz–Thompson estimator.     

MODEL‐BASED DIRECT ESTIMATION OF SMALL‐AREA DISTRIBUTIONS

Much of the small‐area estimation literature focuses on population totals and means. However, users of survey data are often interested in the finite‐population distribution of a survey variable and in the measures (e.g. medians, quartiles, percentiles) that characterize the shape of this distribution at the small‐area level. In this paper we propose a model‐based direct estimator (MBDE, Chandra and Chambers) of the small‐area distribution function. The MBDE is defined as a weighted sum of sample data from the area of interest, with weights derived from the calibrated spline‐based estimate of the finite‐population distribution function introduced by Harms and Duchesne, under an appropriately specified regression model with random area effects. We also discuss the mean squared error estimation of the MBDE. Monte Carlo simulations based on both simulated and real data sets show that the proposed MBDE and its associated mean squared error estimator perform well when compared with alternative estimators of the area‐specific finite‐population distribution function.     

A Bayesian benchmarking of the Scott–Smith model for small areas

When the finite population ‘totals’ are estimated for individual areas, they do not necessarily add up to the known ‘total’ for all areas. Benchmarking (BM) is a technique used to ensure that the totals for all areas match the grand total, which can be obtained from an independent source. BM is desirable to practitioners of survey sampling. BM shifts the small-area estimators to accommodate the constraint. In doing so, it can provide increased precision to the small-area estimators of the finite population means or totals. The Scott–Smith model is used to benchmark the finite population means of small areas. This is a one-way random effects model for a superpopulation, and it is computationally convenient to use a Bayesian approach. We illustrate our method by estimating body mass index using data in the third National Health and Nutrition Examination Survey. Several properties of the benchmarked small-area estimators are obtained using a simulation study.