小域估计的理论和最新进展

小域估计问题是当今抽样调查中的一个热点问题,由于小域样本量很小甚至为零,用传统的直接估计无法得到小域的精确估计,故借助于其他相邻与相似的小域的样本信息和历史信息的间接估计来提高估计的精度,是十分必要的.目前小域估计的主流发展方向是基于模型的小域估计方法,在介绍基于小域层次模型的小域估计方法和基于单元层次模型的小域估计方法的理论基础上,对实际调查中存在的一些小域估计问题以及针对这些实际问题的最近进展进行介绍,具有重要的理论和实践意义.     

分位数回归模型在小域估计中的应用

小域估计问题日益受到社会各界的关注,它通常利用辅助信息和统计模型提高估计的精度。其中最常用的小域模型是混合模型,即利用域随机效应来解释域间变化,但是这种模型要求严格的假定条件,不易于处理实际中存在异常值或重尾现象的小域估计问题。本文将分位数回归模型引入小域估计中,这个模型不需要强的假定条件,可以处理实际中存在异常值或是重尾现象的小域估计问题,并通过一个模拟案例进一步说明了基于分位数回归模型的小域估计方法可以得到更加稳健的估计量．挖掘更多的信息来提高小域估计的精度,是一种比较好的小域估计方法。     

基于分层贝叶斯分析的残疾率小域估计方法

小域估计（Small Area Estimation）是抽样调查领域里一个重要的研究方向,国计民生中的许多重要问题如失业率、传染病的发病率和民意测验等抽样调查都需要采用不同的小域估计方法。本文针对小域估计问题,以估计方法发展脉络为主线,以分层贝叶斯分析的小域估计为重点,对小域估计问题的理论、方法和最新进展进行简述,并利用澳大利亚残疾、老龄化和护理者（SDAC 2003）抽样调查实际数据,从分层贝叶斯分析角度对澳大利亚残疾率进行估计,最后对估计结果进行比较和讨论。     

基于空间模型的小域估计方法

小域估计成为当今抽样调查的热点问题之一，日益受到社会各界的关注。小域估计多采用基于模型的估计方法，其中以线性混合模型最为普遍，这种模型通常假定域随机效应是独立的。但是，在实际各个域之间往往表现出一定的空间相关性，并且这种相关性随着距离的增加而减小，若忽视这种空间效应，估计的精度会大大的降低。本文运用域随机效应为空间相关的空间模型来解决空间数据下的小域估计问题，并用基于这种空间模型的权数的方法得到了目标变量的稳健估计量，很大程度上提高小域估计的精度，是一种比较好的小域估计方法。     

小域估计方法在小品种农作物播种面积统计中的应用

 我国以省级目标总体开展的现行农产量抽样调查,着眼于农作物主要品种的省级推算,而小品种农作物的总体分布比较偏态,往往有效样本量相对不足,不能解决小品种农作物播种面积的推算问题,同时对分县的主要品种农作物播种面积进行的直接推算也不能满足精度要求。现阶段对小品种农作物播种面积的统计方法研究成为农村统计方法制度改革迫切需要研究的课题之一。本文选择了河北省张家口的蔚县,利用小域估计方法对小品种农作物播种面积进行了统计推断,从推断结果看得到了比较好的估计精度。利用蔚县为总体的实际数据进行的抽样仿真分析,从实证的角度阐述了小域估计方法对这一问题的有效性,而且分析结果也表明该方法可以显著提高估计效果。     

基于样本回答率视角下的总体参数估计

文章构建了基于样本回答率视角下的总体参数估计量模型,讨论了总体参数估计量方差及方差的估计,实证检验了估计模型,并分析了样本回答率对总体参数估计精度的影响.     

多目标变量调查的小域的稳健估计量研究

大型的抽样调查不仅是多目标的复杂调查,而且在估计总体目标变量的基础上还需要对其中的一些域的目标变量进行估计,所以小域估计和多目标估计问题一直是抽样调查的热点问题.文章主要利用模型校准权数的方法,解决小域中的多目标估计问题,并得到小域的多个目标变量的稳健估计量.     

遥感辅助的农作物种植面积小域估计方法研究

遥感影像是大数据的一种,利用遥感对农作物播种面积进行估算常采用回归估计量或校准估计量,通常都需要将地面样本数据与遥感分类信息相结合。但对于大多数回归估计量,对省级总体的农作物面积估算只能满足对省级总体的精度要求而不能分解到更小区域,比如县和乡级。本文利用黑龙江省2011年的地面实测样本数据结合遥感分类结果,构建了单元层次的多响应变量的多元回归形式的小域模型,并将小域效应设定为固定形式。这样基于回归估计方法,既可以估算分县的主要作物播种面积,也可以使得各县播种面积估计结果相加就等于回归模型含义下的省级总体的总量估计。对黑龙江省玉米、水稻、大豆分县小域估计结果的精度评价（变异系数C.V）,平均而言均可以满足县级精度要求。本文的结果表明小域估计方法在解决省级总体对全省和分县的农作物种植面积多级估算问题中具有很好的应用。     

基于对数变换的小域的稳健估计量

小域估计是抽样调查的热点问题之一,其主流发展方向是基于模型的小域估计方法。但是这种方法依赖于模型的假定,若假定的模型错误,则估计效果很差。因此,利用对数变换和抽样设计权数得到小域的目标变量的稳健估计量,并通过模拟案例说明基于对数变换的方法是一种稳健有效的小域估计方法。     

抽样调查中的校准估计法

本文梳理总结了校准估计法自首次提出以来的研究成果。理论方法的发展集中在最短距离法、工具向量法和模型校准法三种校准方法的研究上;方法应用的发展体现在对简单参数和复杂参数的校准估计上。对小域估计、无回答、二重抽样等特定抽样问题和总体分位数、总体方差估计中校准估计法的具体应用作了重点梳理介绍。对校准估计法的理论和应用研究前景作了展望。     

An elastic net penalized small area model combining unit- and area-level data for regional hypertension prevalence estimation

Hypertension is a highly prevalent cardiovascular disease. It marks a considerable cost factor to many national health systems. Despite its prevalence, regional disease distributions are often unknown and must be estimated from survey data. However, health surveys frequently lack in regional observations due to limited resources. Obtained prevalence estimates suffer from unacceptably large sampling variances and are not reliable. Small area estimation solves this problem by linking auxiliary data from multiple regions in suitable regression models. Typically, either unit- or area-level observations are considered for this purpose. But with respect to hypertension, both levels should be used. Hypertension has characteristic comorbidities and is strongly related to lifestyle features, which are unit-level information. It is also correlated with socioeconomic indicators that are usually measured on the area-level. But the level combination is challenging as it requires multi-level model parameter estimation from small samples. We use a multi-level small area model with level-specific penalization to overcome this issue. Model parameter estimation is performed via stochastic coordinate gradient descent. A jackknife estimator of the mean squared error is presented. The methodology is applied to combine health survey data and administrative records to estimate regional hypertension prevalence in Germany.     

ROBUST ESTIMATION OF SMALL‐AREA MEANS AND QUANTILES

Small‐area estimation techniques have typically relied on plug‐in estimation based on models containing random area effects. More recently, regression M‐quantiles have been suggested for this purpose, thus avoiding conventional Gaussian assumptions, as well as problems associated with the specification of random effects. However, the plug‐in M‐quantile estimator for the small‐area mean can be shown to be the expected value of this mean with respect to a generally biased estimator of the small‐area cumulative distribution function of the characteristic of interest. To correct this problem, we propose a general framework for robust small‐area estimation, based on representing a small‐area estimator as a functional of a predictor of this small‐area cumulative distribution function. Key advantages of this framework are that it naturally leads to integrated estimation of small‐area means and quantiles and is not restricted to M‐quantile models. We also discuss mean squared error estimation for the resulting estimators, and demonstrate the advantages of our approach through model‐based and design‐based simulations, with the latter using economic data collected in an Australian farm survey.     

Information theoretic methods in small domain estimation

Small area estimation techniques are becoming increasingly used in survey applications to provide estimates for local areas of interest. The objective of this article is to develop and apply Information Theoretic (IT)-based formulations to estimate small area business and trade statistics. More specifically, we propose a Generalized Maximum Entropy (GME) approach to the problem of small area estimation that exploits auxiliary information relating to other known variables on the population and adjusts for consistency and additivity. The GME formulations, combining information from the sample together with out-of-sample aggregates of the population of interest, can be particularly useful in the context of small area estimation, for both direct and model-based estimators, since they do not require strong distributional assumptions on the disturbances. The performance of the proposed IT formulations is illustrated through real and simulated datasets.     

Combining information from multiple surveys by using regression for efficient small domain estimation

Summary.  In sample surveys of finite populations, subpopulations for which the sample size is too small for estimation of adequate precision are referred to as small domains. Demand for small domain estimates has been growing in recent years among users of survey data. We explore the possibility of enhancing the precision of domain estimators by combining comparable information collected in multiple surveys of the same population. For this, we propose a regression method of estimation that is essentially an extended calibration procedure whereby comparable domain estimates from the various surveys are calibrated to each other. We show through analytic results and an empirical study that this method may greatly improve the precision of domain estimators for the variables that are common to these surveys, as these estimators make effective use of increased sample size for the common survey items. The design-based direct estimators proposed involve only domain-specific data on the variables of interest. This is in contrast with small domain (mostly small area) indirect estimators, based on a single survey, which incorporate through modelling data that are external to the targeted small domains. The approach proposed is also highly effective in handling the closely related problem of estimation for rare population characteristics.     

M-quantile models with application to poverty mapping

Over the last decade there has been growing demand for estimates of population characteristics at small area level. Unfortunately, cost constraints in the design of sample surveys lead to small sample sizes within these areas and as a result direct estimation, using only the survey data, is inappropriate since it yields estimates with unacceptable levels of precision. Small area models are designed to tackle the small sample size problem. The most popular class of models for small area estimation is random effects models that include random area effects to account for between area variations. However, such models also depend on strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow for outlier robust inference. An alternative approach to small area estimation that is based on the use of M-quantile models was recently proposed by Chambers and Tzavidis (Biometrika 93(2):255–268, 2006) and Tzavidis and Chambers (Robust prediction of small area means and distributions. Working paper, 2007). Unlike traditional random effects models, M-quantile models do not depend on strong distributional assumption and automatically provide outlier robust inference. In this paper we illustrate for the first time how M-quantile models can be practically employed for deriving small area estimates of poverty and inequality. The methodology we propose improves the traditional poverty mapping methods in the following ways: (a) it enables the estimation of the distribution function of the study variable within the small area of interest both under an M-quantile and a random effects model, (b) it provides analytical, instead of empirical, estimation of the mean squared error of the M-quantile small area mean estimates and (c) it employs a robust to outliers estimation method. The methodology is applied to data from the 2002 Living Standards Measurement Survey (LSMS) in Albania for estimating (a) district level estimates of the incidence of poverty in Albania, (b) district level inequality measures and (c) the distribution function of household per-capita consumption expenditure in each district. Small area estimates of poverty and inequality show that the poorest Albanian districts are in the mountainous regions (north and north east) with the wealthiest districts, which are also linked with high levels of inequality, in the coastal (south west) and southern part of country. We discuss the practical advantages of our methodology and note the consistency of our results with results from previous studies. We further demonstrate the usefulness of the M-quantile estimation framework through design-based simulations based on two realistic survey data sets containing small area information and show that the M-quantile approach may be preferable when the aim is to estimate the small area distribution function.     

The use of power transformations in small area estimation

Sample surveys are usually designed and analysed to produce estimates for larger areas. Nevertheless, sample sizes are often not large enough to give adequate precision for small area estimates of interest. To overcome such difficulties, borrowing strength from related small areas via modelling becomes essential. In line with this, we propose components of variance models with power transformations for small area estimation. This paper reports the results of a study aimed at incorporating the power transformation in small area estimation for improving the quality of small area predictions. The proposed methods are demonstrated on satellite data in conjunction with survey data to estimate mean acreage under a specified crop for counties in Iowa.     

On prediction of population and subpopulation characteristics for future periods

The estimation or prediction of population characteristics based on the sample information is the key issue in survey sampling. If the sample sizes in subpopulations (domains) are large enough, similar methods as used for the whole population can be used to estimate or to predict subpopulations characteristics as well. To estimate or to predict characteristics of domains with small or even zero sample sizes, small area estimation methods “borrowing strength” from other subpopulations or time periods are widely used. We extend this problem and study methods of prediction of future population and subpopulations’ characteristics based on the longitudinal data.     

Small area estimates for cross-classifications

Summary.  We develop a class of log-linear structural models that is suited to estimation of small area cross-classified counts based on survey data. This allows us to account for various associ- ation structures within the data and includes as a special case the restricted log-linear model underlying structure preserving estimation. The effect of survey design can be incorporated into estimation through the specification of an unbiased direct estimator and its associated covariance structure. We illustrate our approach by applying it to estimation of small area labour force characteristics in Norway.     

Functional calibration estimation by the maximum entropy on the mean principle

We extend the problem of obtaining an estimator for the finite population mean parameter incorporating complete auxiliary information through calibration estimation in survey sampling under a functional data framework. The functional calibration sampling weights of the estimator are obtained by matching the calibration estimation problem with the maximum entropy on the mean – MEM – principle. In particular, the calibration estimation is viewed as an infinite-dimensional linear inverse problem following the structure of the MEM approach. We give a precise theoretical setting and estimate the functional calibration weights assuming, as prior measures, the centred Gaussian and compound Poisson random measures. Additionally, through a simple simulation study, we show that the proposed functional calibration estimator improves its accuracy compared with the Horvitz–Thompson one.