Modelling Group Heterogeneity for Small Area Estimation Using M‐Quantiles

Small area estimation typically requires model‐based methods that depend on isolating the contribution to overall population heterogeneity associated with group (i.e. small area) membership. One way of doing this is via random effects models with latent group effects. Alternatively, one can use an M‐quantile ensemble model that assigns indices to sampled individuals characterising their contribution to overall sample heterogeneity. These indices are then aggregated to form group effects. The aim of this article is to contrast these two approaches to characterising group effects and to illustrate them in the context of small area estimation. In doing so, we consider a range of different data types, including continuous data, count data and binary response data.     

Benchmarked Estimators for a Small Area Mean Under a Onefold Nested Regression Model

In this paper, we modify small area estimators, based on the unit‐level model, so that they add up to reliable higher‐level estimates of population totals. These modifications result in benchmarked small area estimators. We consider two benchmarking procedures. One is based on augmenting the unit‐level model with a suitable variable. The other one uses the calibrated weights of the direct estimators that are reliable at the higher levels. These weights are used in estimators that are based on the aggregation of the unit‐level model for each small area. The mean squared error estimators of the proposed benchmarked estimators are obtained by suitably modifying those associated with the corresponding non benchmarked estimators. The properties of the estimators are evaluated via simulation.     

Localised Estimates of Dynamics of Multi‐dimensional Disadvantage: An Application of the Small Area Estimation Technique Using Australian Survey and Census Data

Deep and persistent disadvantage is an important, but statistically rare, phenomenon in the population, and sample sizes are usually not large enough to provide reliable estimates for disaggregated analysis. Survey samples are typically designed to produce estimates of population characteristics of planned areas. The sample sizes are calculated so that the survey estimator for each of the planned areas is of a desired level of precision. However, in many instances, estimators are required for areas of the population for which the survey providing the data was unplanned. Then, for areas with small sample sizes, direct estimation of population characteristics based only on the data available from the particular area tends to be unreliable. This has led to the development of a class of indirect estimators that make use of information from related areas through modelling. A model is used to link similar areas to enhance the estimation of unplanned areas; in other words, they borrow strength from the other areas. Doing so improves the precision of estimated characteristics in the small area, especially in areas with smaller sample sizes. Social science researchers have increasingly employed small area estimation to provide localised estimates of population characteristics from surveys. We explore how to extend this approach within the context of deep and persistent disadvantage in Australia. We find that because of the unique circumstances of the Australian population distribution, direct estimates of disadvantage have substantial variation, but by applying small area estimation, there are significant improvements in precision of estimates.     

Small Area Estimation for Disease Prevalence Mapping

Small area estimation (SAE) entails estimating characteristics of interest for domains, often geographical areas, in which there may be few or no samples available. SAE has a long history and a wide variety of methods have been suggested, from a bewildering range of philosophical standpoints. We describe design-based and model-based approaches and models that are specified at the area level and at the unit level, focusing on health applications and fully Bayesian spatial models. The use of auxiliary information is a key ingredient for successful inference when response data are sparse, and we discuss a number of approaches that allow the inclusion of covariate data. SAE for HIV prevalence, using data collected from a Demographic Health Survey in Malawi in 2015–2016, is used to illustrate a number of techniques. The potential use of SAE techniques for outcomes related to coronavirus disease 2019 is discussed.     

Benchmarking Warehousing and Distribution Operations: An Input-Output Approach

We developan input-output model of a warehouse system to assess operationalefficiency. Our model simultaneously accounts for all of thecritical resources (labor, space, storage and handling equipment)and the different workload requirements (broken case, full caseand pallet picking, storage and order accumulation) of a warehouse.We collected extensive data on 57 warehouse and distributionfacilities from a variety of industries, including auto parts,dental and office supplies, electronics, fine papers, hardware,health care, industrial packaging, mail order apparel, officemachines, photographic supplies, and wholesale drugs, and usedthe model to assess and compare their efficiencies. We offer3 conclusions based on a statistical analysis of the operatingefficiencies obtained from several models: Smaller warehouses tend to be more efficient than larger warehouses.Warehouses using lower levels of automation tend to be moreefficient. This association is more pronounced in small firms.Unionization is not negatively associated with efficiencyand in fact may actually contribute to higher efficiency.     

A Comparison of Methods for Poverty Estimation in Developing Countries

Small area estimation is a widely used indirect estimation technique for micro‐level geographic profiling. Three unit level small area estimation techniques—the ELL or World Bank method, empirical best prediction (EBP) and M‐quantile (MQ) — can estimate micro‐level Foster, Greer, & Thorbecke (FGT) indicators: poverty incidence, gap and severity using both unit level survey and census data. However, they use different assumptions. The effects of using model‐based unit level census data reconstructed from cross‐tabulations and having no cluster level contextual variables for models are discussed, as are effects of small area and cluster level heterogeneity. A simulation‐based comparison of ELL, EBP and MQ uses a model‐based reconstruction of 2000/2001 data from Bangladesh and compares bias and mean square error. A three‐level ELL method is applied for comparison with the standard two‐level ELL that lacks a small area level component. An important finding is that the larger number of small areas for which ELL has been able to produce sufficiently accurate estimates in comparison with EBP and MQ has been driven more by the type of census data available or utilised than by the model per se.     

Small domain statistics: a review

Local data are required at short intervals of time mainly for undertaking regional development projects on ascertaining area-wise socio-economic requirements, proper devolution of funds and resources from central pools and allocation of legislative seats. A census is an infrequent source for them and is also incomprehensive. Official records and registers are a second source but are generally inadequate. Sample surveys are a recognized third alternative. But even for large total sample sizes, when numerous local areas are involved, many are not represented well enough in samples. Consequently, for totals of small areas classical survey estimates turn out inefficient having large mean square errors admitting uselessly wide confidence intervals. Improved estimation procedures however are rapidly emerging based on postulated models which encourage borrowing strength from samples outside local areas and from past data. A brief review is attempted illustrating applications.     

Small Area Quantile Estimation

Sample surveys are widely used to obtain information about totals, means, medians and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific geographic areas and socio‐demographic groups. When the surveys are conducted at national or similarly high levels, a probability sampling can result in just a few sampling units from many unplanned subpopulations at the design stage. Cost considerations may also lead to low sample sizes from individual small areas. Estimating the parameters of these subpopulations with satisfactory precision and evaluating their accuracy are serious challenges for statisticians. To overcome the difficulties, statisticians resort to pooling information across the small areas via suitable model assumptions, administrative archives and census data. In this paper, we develop an array of small area quantile estimators. The novelty is the introduction of a semiparametric density ratio model for the error distribution in the unit‐level nested error regression model. In contrast, the existing methods are usually most effective when the response values are jointly normal. We also propose a resampling procedure for estimating the mean square errors of these estimators. Simulation results indicate that the new methods have superior performance when the population distributions are skewed and remain competitive otherwise.     

绩效标杆模型在输配电价管制中的应用

管制者在制定输配电价格时,常采用基于RPI-X公式的价格上限、收益上限、与标尺竞争管制,对于效率因数X的确定,许多国家倾向于应用基于企业的相对效率制定绩效标杆来确定。前沿绩效标杆方法主要运用DEA求出绩效较好的企业,作为参照绩效。本文讨论DEA方法在绩效标杆法中的应用,并用绩效标杆法解决电价管制的问题。     

Limits to the Implementation of Benchmarking Through KPIs in UK Construction Policy: Insights from game theory

Abstract

Benchmarking through the use of key performance indicators (KPIs) has been an important part of the UK government's market-oriented reforms to improve efficiency across the public sector and in other areas such as construction where government is a major client. However, government attempts to implement construction KPIs have not followed the expected course. We argue that insights from game theory show that the initial plan for construction benchmarking failed to take account of the strategic value of the information collected and was not implementable because the sharing of information by construction suppliers with their clients was a dominated strategy.     

Robust Small Area Estimation under Spatial Non‐stationarity

The effective use of spatial information in a regression‐based approach to small area estimation is an important practical issue. One approach to account for geographic information is by extending the linear mixed model to allow for spatially correlated random area effects. An alternative is to include the spatial information by a non‐parametric mixed models. Another option is geographic weighted regression where the model coefficients vary spatially across the geography of interest. Although these approaches are useful for estimating small area means efficiently under strict parametric assumptions, they can be sensitive to outliers. In this paper, we propose robust extensions of the geographically weighted empirical best linear unbiased predictor. In particular, we introduce robust projective and predictive estimators under spatial non‐stationarity. Mean squared error estimation is performed by two analytic approaches that account for the spatial structure in the data. Model‐based simulations show that the methodology proposed often leads to more efficient estimators. Furthermore, the analytic mean squared error estimators introduced have appealing properties in terms of stability and bias. Finally, we demonstrate in the application that the new methodology is a good choice for producing estimates for average rent prices of apartments in urban planning areas in Berlin.     

温压战斗部爆炸冲击波毁伤小子样试验鉴定分析

针对温压战斗部爆炸冲击波毁伤的试验鉴定问题,提出冲击波毁伤的试验鉴定即为对毁伤参数所服从分布以及分布参数的统计推断问题,并进一步给出温压战斗部毁伤小子样试验鉴定的基本思路,重点对利用Bayes理论开展统计推断的方法进行了研究,介绍了两种验前分布的求取方法,并对Bayes估计理论进行了深入探讨,介绍了点估计和区间估计求取的具体方法。     

机械装备制造业配件与物流标杆运营分析

选取卡特彼勒公司作为标杆企业进行探讨分析,系统研究了其配件与物流的做法,并由此得出对中国机械装备制造业发展的启示。     

Some Variants of Constrained Estimation in Finite Population Sampling

This is a review article that unifies several important examples using constrained optimisation techniques. The basic tools are three simple mathematical optimisation results subject to certain constraints. Applications include calibration, benchmarking in small area estimation and imputation. A final illustration is constrained optimisation under a general divergence loss.     

Estimation of Randomisation Mean Square Error in Small Area Estimation

In this article, we propose a new method for estimating the randomisation (design‐based) mean squared error (DMSE) of model‐dependent small area predictors. Analogously to classical survey sampling theory, the DMSE considers the finite population values as fixed numbers and accounts for the MSE of small area predictors over all possible sample selections. The proposed method models the true DMSE as computed for synthetic populations and samples drawn from them, as a function of known statistics and then applies the model to the original sample. Several simulation studies for the linear area‐level model and the unit‐level mixed logistic model illustrate the performance of the proposed method and compare it with the performance of other DMSE estimators proposed in the literature.     

Towards a Routine External Evaluation Protocol for Small Area Estimation

Statistical criteria are needed by which to evaluate the potential success or failure of applications of small area estimation. A necessary step to achieve this is a protocol—a series of steps—by which to assess whether an instance of small area estimation has given satisfactory results or not. Most customary attempts at evaluation of small area techniques have deficiencies. Often, evaluation is not attempted. Every small area study requires an external evaluation. With proper planning, this can be routinely achieved, although at some cost, amounting to some sacrifice of efficiency of global estimates. We propose a Routine External Evaluation Protocol to allow us to judge whether, in a given survey, small area estimation has led to accurate results and sound inference.     

对住宅小区环境设计的思考

随着住宅小区买方市场的形成,消费者对住宅小区和小区环境提出更高的要求。本文着重从设计程序、追求角度、模仿角度和投资比例等几个方面谈了住宅小区环境设计中的几个常见误区及避免措施。     

Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model

Assessing regional population compositions is an important task in many research fields. Small area estimation with generalized linear mixed models marks a powerful tool for this purpose. However, the method has limitations in practice. When the data are subject to measurement errors, small area models produce inefficient or biased results since they cannot account for data uncertainty. This is particularly problematic for composition prediction, since generalized linear mixed models often rely on approximate likelihood inference. Obtained predictions are not reliable. We propose a robust multivariate Fay–Herriot model to solve these issues. It combines compositional data analysis with robust optimization theory. The nonlinear estimation of compositions is restated as a linear problem through isometric logratio transformations. Robust model parameter estimation is performed via penalized maximum likelihood. A robust best predictor is derived. Simulations are conducted to demonstrate the effectiveness of the approach. An application to alcohol consumption in Germany is provided.     

对山区小型水利工程的浅论

上世纪七、八十年代修建的工程,主要由民工投劳完成,工程建设标准低,配套不完善。小型水利工程的建设,可促进山丘区水利持续发展,实现农业增效、农民增收、农村经济跨越式发展的良好局面。     

Robust Hierarchical Bayes Small Area Estimation for the Nested Error Linear Regression Model

Standard model‐based small area estimates perform poorly in presence of outliers. Sinha & Rao ( 2009 ) developed robust frequentist predictors of small area means. In this article, we present a robust Bayesian method to handle outliers in unit‐level data by extending the nested error regression model. We consider a finite mixture of normal distributions for the unit‐level error to model outliers and produce noninformative Bayes predictors of small area means. Our modelling approach generalises that of Datta & Ghosh ( 1991 ) under the normality assumption. Application of our method to a data set which is suspected to contain an outlier confirms this suspicion, correctly identifies the suspected outlier and produces robust predictors and posterior standard deviations of the small area means. Evaluation of several procedures including the M‐quantile method of Chambers & Tzavidis ( 2006 ) via simulations shows that our proposed method is as good as other procedures in terms of bias, variability and coverage probability of confidence and credible intervals when there are no outliers. In the presence of outliers, while our method and Sinha–Rao method perform similarly, they improve over the other methods. This superior performance of our procedure shows its dual (Bayes and frequentist) dominance, which should make it attractive to all practitioners, Bayesians and frequentists, of small area estimation.