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J N K Rao - One of the best experts on this subject based on the ideXlab platform.
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a comparison of Small Area Estimation methods for poverty mapping
Statistics in Transition New Series, 2016Co-Authors: Maria Guadarrama, Isabel Molina, J N K RaoAbstract:Poverty maps are an important source of information on the regional distribution of poverty and are currently used to support regional policy making and to allocate funds to local jurisdictions. But obtaining accurate poverty maps at low levels of disaggregation is not straightforward because of insufficient sample size of official surveys in some of the target regions. Direct estimates, obtained with the region-specific sample data, are unstable in the sense of having very large sampling errors for regions with Small sample size. Very unstable poverty estimates might make the seemingly poorer regions in one period appear as the richer in the next period, which can be inconsistent. On the other hand, very stable but biased estimates (e.g., too homogeneous across regions) might make identification of the poorer regions difficult. Here we review the main Small Area Estimation methods for poverty mapping. In particular, we consider direct Estimation, the Fay-Herriot Area level model, the method of Elbers, Lanjouw and Lanjouw (2003) used by the World Bank, the empirical Best/Bayes (EB) method of Molina and Rao (2010) and its extension, the Census EB, and finally the hierarchical Bayes proposal of Molina, Nandram and Rao (2014). We put ourselves in the point of view of a practitioner and discuss, as objectively as possible, the benefits and drawbacks of each method, illustrating some of them through simulation studies.
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Small Area Estimation of poverty indicators
Canadian Journal of Statistics-revue Canadienne De Statistique, 2010Co-Authors: Isabel Molina, J N K RaoAbstract:The authors propose to estimate nonlinear Small Area population parameters by using the empirical Bayes (best) method, based on a nested error model. They focus on poverty indicators as particular nonlinear parameters of interest, but the proposed methodology is applicable to general nonlinear parameters. They use a parametric bootstrap method to estimate the mean squared error of the empirical best estimators. They also study Small sample properties of these estimators by model-based and design-based simulation studies. Results show large reductions in mean squared error relative to direct Area-specific estimators and other estimators obtained by “simulated” censuses. The authors also apply the proposed method to estimate poverty incidences and poverty gaps in Spanish provinces by gender with mean squared errors estimated by the mentioned parametric bootstrap method. For the Spanish data, results show a significant reduction in coefficient of variation of the proposed empirical best estimators over direct estimators for practically all domains. The Canadian Journal of Statistics 38: 369–385; 2010 © 2010 Statistical Society of Canada
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robust Small Area Estimation
Canadian Journal of Statistics-revue Canadienne De Statistique, 2009Co-Authors: Sanjoy K Sinha, J N K RaoAbstract:Small Area Estimation has received considerable attention in recent years because of growing demand for Small Area statistics. Basic Area-level and unit-level models have been studied in the literature to obtain empirical best linear unbiased prediction (EBLUP) estimators of Small Area means. Although this classical method is useful for estimating the Small Area means efficiently under normality assumptions, it can be highly influenced by the presence of outliers in the data. In this article, the authors investigate the robustness properties of the classical estimators and propose a resistant method for Small Area Estimation, which is useful for downweighting any influential observations in the data when estimating the model parameters. To estimate the mean squared errors of the robust estimators of Small Area means, a parametric bootstrap method is adopted here, which is applicable to models with block diagonal covariance structures. Simulations are carried out to study the behaviour of the proposed robust estimators in the presence of outliers, and these estimators are also compared to the EBLUP estimators. Performance of the bootstrap mean squared error estimator is also investigated in the simulation study. The proposed robust method is also applied to some real data to estimate crop Areas for counties in Iowa, using farm-interview data on crop Areas and LANDSAT satellite data as auxiliary information. The Canadian Journal of Statistics 37: 381–399; 2009 © 2009 Statistical Society of Canada L'Estimation de petits domaines a rec cu considerablement d'attention ces dernieres annees en raison de la demande croissante de statistiques regionales. Les modeles au niveau des domaines et des unites ont deja ete etudies dans la litterature et les meilleurs estimateurs lineaires sans biais empiriques (EBLUP) pour les petits domaines ont ete obtenus. Quoique cette methode classique est utile pour estimer les moyennes regionales de fac con efficace sous l'hypothese de normalite, ses resultats sont grandement influences par la presente de donnees aberrantes. Dans cet article, les auteurs etudient les proprietes de robustesse des estimateurs classiques et ils proposent une methode robuste pour l'Estimation de petits domaines qui diminue le poids associe aux observations influentes lors de l'Estimation des parametres du modele. Afin d'estimer l'erreur quadratique moyenne des estimateurs robustes des moyennes regionales, une methode d'auto-amorc cage parametrique est utilisee. Cette methode peut etre utilisee aux modeles dont la structure de covariance est bloc diagonale. Des simulations sont faites pour etudier le comportement des estimateurs robustes proposes en presence de valeurs aberrantes et aussi pour les comparer aux estimateurs EBLUP. La performance de l'estimateur “boostrap” de l'erreur quadratique moyenne est aussi etudiee dans cette etude de simulations. Cette methode robuste est appliquee a l'Estimation de la superficie des cultures pour les comtes de l'Iowa en se basant sur des entrevues au niveau des fermes et en utilisant les donnees provenant du satellite LANDSAT comme information auxiliaire. La revue canadienne de statistique 37: 381–399; 2009 © 2009 Societe statistique du Canada
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pseudo hierarchical bayes Small Area Estimation combining unit level models and survey weights
Journal of Statistical Planning and Inference, 2003Co-Authors: Yong You, J N K RaoAbstract:Unit level random effects models, such as nested error regression models, are often used in Small Area Estimation to obtain efficient model-based estimators of Small Area means. Such estimators typically do not make use of the survey weights. As a result, the estimators are not design consistent unless the sampling design is self-weighting within Areas. In this paper, a two-step approach is developed to obtain design-consistent Small Area estimates by utilizing the survey weights. In the first step, conditional posterior means and conditional posterior variances of the Small Area means are derived from the aggregated Area level model, assuming that the variance components and regression parameters (fixed effects) are known. In the second step, posterior estimates of the variance components are obtained from the unit level model. Three different methods of estimating the regression parameters are studied. Combining the two Estimation steps leads to pseudo-hierarchical Bayes estimators for the Small Area means. The proposed methods are evaluated on a real data set studied by Battese et al. (J. Amer. Statist. Assoc. 83 (1988) 28).
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Small Area Estimation
2003Co-Authors: J N K RaoAbstract:List of Figures. List of Tables. Foreword. Preface. 1. Introduction. What is a Small Area? Demand for Small Area Statistics. Traditional Indirect Estimators. Small Area Models. Model-Based Estimation. Some Examples. 2. Direct Domain Estimation. Introduction. Design-based Approach. Estimation of Totals. Domain Estimation. Modified Direct Estimators. Design Issues. Proofs. 3. Traditional Demographic Methods. Introduction. Symptomatic Accounting Techniques. Regression Symptomatic Procedures. Dual-system Estimation of Total Population. Derivation of Average MSEs. 4. Indirect Domain Estimation. Introduction. Synthetic Estimation. Composite Estimation. James-Stein Method. Proofs. 5. Small Area Models. Introduction. Basic Area Level (Type A) Mode l. Basic Unit Level (Type B) Model. Extensions: Type A Models. Extensions: Type B Models. Generalized Linear Mixed Models. 6. Empirical Best Linear Unbiased Prediction: Theory. Introduction. General Linear Mixed Model. Block Diagonal Covariance Structure. Proofs. 7. EBLUP: Basic Models. Basic Area Level Model. Basic Unit Level Model. 8. EBLUP: Extensions. Multivariate Fay-Herriot Model. Correlated Sampling Errors. Time Series and Cross-sectional Models. Spatial Models. Multivariate Nested Error Regression Model. Random Error Variances Linear Model. Two-fold Nested Error Regression Model. Two-level Model. 9. Empirical Bayes (EB) Method. Introduction. Basic Area Level Model. Linear Mixed Models. Binary Data. Disease Mapping. Triple-goal Estimation. Empirical Linear Bayes. Constrained LB. Proofs. 10. Hierarchical Bayes (HB) Method. Introduction. MCMC Methods. Basic Area Level Model. Unmatched Sampling and Linking Area Level Models. Basic Unit Level Model. General ANOVA Model. Two-level Models. Time Series and Cross-sectional Models. Multivariate Models. Disease Mapping Models. Binary Data. Exponential Family Models. Constrained HB. Proofs. References. Author Index. Subject Index.
Malay Ghosh - One of the best experts on this subject based on the ideXlab platform.
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shrinkage Estimation with singular priors and an application to Small Area Estimation
Journal of Multivariate Analysis, 2021Co-Authors: Ryumei Nakada, Malay Ghosh, Tatsuya Kubokawa, Sayar KarmakarAbstract:Abstract The paper considers Estimation of the multivariate normal mean under a multivariate normal prior with a singular precision matrix. Such a setup appears in the multi-task averaging, serial and spatial smoothing problems. The empirical and hierarchical Bayes estimators shrink the maximum likelihood estimator by projecting it to the null space of the precision matrix. Conditions for minimaxity are given for the estimators proposed in this paper. The singular prior is applied to the Fay–Herriot Small Area Estimation model with random effects having the singular distribution. Second-order approximation of the conditional mean squared error of the empirical Bayes estimator and its second-order unbiased estimator are derived. Numerical simulations confirm that the derived estimators perform well under the situation when there is a spatial correlation in the sample.
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Small Area Estimation its evolution in five decades
Statistics in Transition New Series, 2020Co-Authors: Malay GhoshAbstract:The paper is an attempt to trace some of the early developments of Small Area Estimation. The basic papers such...
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modeling random effects using global local shrinkage priors in Small Area Estimation
Journal of the American Statistical Association, 2018Co-Authors: Xueying Tang, Malay Ghosh, J SedranskAbstract:Small Area Estimation is becoming increasingly popular for survey statisticians. One very important program is Small Area Income and Poverty Estimation undertaken by the United States Bureau of the...
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two stage benchmarking as applied to Small Area Estimation
Test, 2013Co-Authors: Malay Ghosh, Rebecca C SteortsAbstract:There has been recent growth in Small Area Estimation due to the need for more precise Estimation of Small geographic Areas, which has led to groups such as the U.S. Census Bureau, Google, and the RAND corporation utilizing Small Area-Estimation procedures. We develop a novel two-stage benchmarking methodology using a single weighted squared error loss function that combines the loss at the unit level and the Area level without any specific distributional assumptions. This loss is considered while benchmarking the weighted means at each level or both the weighted means and weighted variability at the unit level. Furthermore, we provide multivariate extensions for benchmarking weighted means at both levels. The behavior of our methods is analyzed using a complex study from the National Health Interview Survey (NHIS) from 2000, which estimates the proportion of people that do not have health insurance for many domains of an Asian subpopulation. Finally, the methodology is explored via simulated data under the proposed model. Ultimately, three proposed benchmarked Bayes estimators do not dominate each other, leaving much exploration for further understanding of such complex studies such as the choice of weights, optimal algorithms for efficiency, as well as extensions to multi-stage benchmarking methods.
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two stage benchmarking as applied to Small Area Estimation
arXiv: Methodology, 2013Co-Authors: Malay Ghosh, Rebecca C SteortsAbstract:There has been recent growth in Small Area Estimation due to the need for more precise Estimation of Small geographic Areas, which has led to groups such as the U.S. Census Bureau, Google, and the RAND corporation utilizing Small Area Estimation procedures. We develop novel two-stage benchmarking methodology using a single weighted squared error loss function that combines the loss at the unit level and the Area level without any specific distributional assumptions. We consider this loss while benchmarking the weighted means at each level or both the weighted means and weighted variability at the unit level. Multivariate extensions are immediate. We analyze the behavior of our methods using a complex study from the National Health Interview Survey (NHIS) from 2000, which estimates the proportion of people that do not have health insurance for many domains of an Asian subpopulation. Finally, the methodology is explored via simulated data under the proposed model. We ultimately conclude that three proposed benchmarked Bayes estimators do not dominate each other, leaving much exploration for future research.
Nicola Salvati - One of the best experts on this subject based on the ideXlab platform.
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semiparametric Small Area Estimation for binary outcomes with application to unemployment Estimation for local authorities in the uk
Journal of The Royal Statistical Society Series A-statistics in Society, 2016Co-Authors: Ray Chambers, Nicola Salvati, Nikos TzavidisAbstract:A new semiparametric and robust approach to Small Area Estimation for discrete outcomes is proposed. The methodology represents an efficient and easily computed alternative to prediction by using a generalized linear mixed model and is based on an extension of M-quantile regression. In addition, two estimators of the prediction mean-squared error are described: one based on Taylor linearization and another based on the block bootstrap. The methodology proposed is applied to UK annual Labour Force Survey data for estimating the proportion of the unemployed in local authorities in the UK. The properties of estimators are further empirically assessed in model-based simulations.
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outlier robust Small Area Estimation
Journal of The Royal Statistical Society Series B-statistical Methodology, 2014Co-Authors: Ray Chambers, Nicola Salvati, Hukum Chandra, Nikos TzavidisAbstract:type="main" xml:id="rssb12019-abs-0001"> Recently proposed outlier robust Small Area estimators can be substantially biased when outliers are drawn from a distribution that has a different mean from that of the rest of the survey data. This naturally leads one to consider an outlier robust bias correction for these estimators. We develop this idea, proposing two different analytical mean-squared error estimators for the ensuing bias-corrected outlier robust estimators. Simulations based on realistic outlier-contaminated data show that the bias correction proposed often leads to more efficient estimators. Furthermore, the mean-squared error Estimation methods proposed appear to perform well with a variety of outlier robust Small Area estimators.
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robust Small Area Estimation and oversampling in the Estimation of poverty indicators
Survey research methods, 2012Co-Authors: Caterina Giusti, Monica Pratesi, Stefano Marchetti, Nicola SalvatiAbstract:There has been rising interest in research on poverty mapping over the last decade, with the European Union proposing a core of statistical indicators on poverty commonly known as Laeken Indicators. They include the incidence and the intensity of poverty for a set of domains (e.g. young people, unemployed people). The EU-SILC (European Union - Statistics on Income and Living Conditions) survey represents the most important source of information to estimate these poverty indicators at national or regional level (NUTS 1-2 level). However, local policy makers also require statistics on poverty and living conditions at lower geographical/domain levels, but estimating poverty indicators directly from EU-SILC for these domains often leads to inaccurate estimates. To overcome this problem there are two main strategies: i. increasing the sample size of EU-SILC so that direct estimates become reliable and ii. resort to Small Area Estimation techniques. In this paper we compare these two alternatives: with the availability of an oversampling of the EU-SILC survey for the province of Pisa, obtained as a side result of the SAMPLE project (Small Area Methods for Poverty and Living Conditions, http://www.sample-project.eu/), we can compute reliable direct estimates that can be compared to Small Area estimates computed under the M-quantile approach. Results show that the M-quantile Small Area estimates are comparable in terms of efficiency and precision to direct estimates using oversample data. Moreover, considering the oversample estimates as a benchmark, we show how direct estimates computed without the oversample have larger errors as well as larger estimated mean squared errors than corresponding M-quantile estimates.
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Small Area Estimation under spatial nonstationarity
Computational Statistics & Data Analysis, 2012Co-Authors: Hukum Chandra, Nicola Salvati, Ray Chambers, Nikos TzavidisAbstract:A geographical weighted empirical best linear unbiased predictor (GWEBLUP) for a Small Area average is proposed, and an estimator of its conditional mean squared error is developed. The popular empirical best linear unbiased predictor under the linear mixed model is obtained as a special case of the GWEBLUP. Empirical results using both model-based and design-based simulations, with the latter based on two real data sets, show that the GWEBLUP predictor can lead to efficiency gains when spatial nonstationarity is present in the data. A practical gain from using the GWEBLUP is in Small Area Estimation for out of sample Areas. In this case the efficient use of geographical information can potentially improve upon conventional synthetic Estimation.
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Small Area Estimation of the mean using non parametric m quantile regression a comparison when a linear mixed model does not hold
Journal of Statistical Computation and Simulation, 2011Co-Authors: Nicola Salvati, M G Ranalli, Monica PratesiAbstract:The demand for reliable statistics in subpopulations, when only reduced sample sizes are available, has promoted the development of Small Area Estimation methods. In particular, an approach that is now widely used is based on the seminal work by Battese et al. [An error-components model for prediction of county crop Areas using survey and satellite data, J. Am. Statist. Assoc. 83 (1988), pp. 28–36] that uses linear mixed models (MM). We investigate alternatives when a linear MM does not hold because, on one side, linearity may not be assumed and/or, on the other, normality of the random effects may not be assumed. In particular, Opsomer et al. [Nonparametric Small Area Estimation using penalized spline regression, J. R. Statist. Soc. Ser. B 70 (2008), pp. 265–283] propose an estimator that extends the linear MM approach to the case in which a linear relationship may not be assumed using penalized splines regression. From a very different perspective, Chambers and Tzavidis [M-quantile models for Small Area...
Domingo Morales - One of the best experts on this subject based on the ideXlab platform.
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Small Area Estimation of poverty indicators under partitioned Area level time models
Sort-statistics and Operations Research Transactions, 2015Co-Authors: Domingo Morales, Maria Chiara Pagliarella, Renato SalvatoreAbstract:This paper deals with Small Area Estimation of poverty indicators. Small Area estimators of these quantities are derived from partitioned time-dependent Area-level linear mixed models. The introduced models are useful for modelling the different behaviour of the target variable by sex or any other dichotomic characteristic. The mean squared errors are estimated by explicit formulas. An application to data from the Spanish Living Conditions Survey is given.
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multinomial based Small Area Estimation of labour force indicators
Statistical Modelling, 2013Co-Authors: Esther Lopezvizcaino, Maria Jose Lombardia, Domingo MoralesAbstract:This paper deals with Small Area Estimation of labour force characteristics like totals of employed, unemployed and inactive people and unemployment rates. Small Area estimators of these quantities are derived from a multinomial logit mixed model with independent random effects on the categories of the response vector. The mean squared errors are estimated both by explicit formulas and by bootstrap methods. Two simulation experiments designed to analyze the behaviour of the introduced estimators have been carried out. Finally, an application to real data from the Spanish Labour Force Survey of Galicia is given.
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Small Area Estimation with spatio temporal fay herriot models
Computational Statistics & Data Analysis, 2013Co-Authors: Yolanda Marhuenda, Isabel Molina, Domingo MoralesAbstract:Small Area Estimation is studied under a spatio-temporal Fay-Herriot model. Model fitting based on restricted maximum likelihood is described and empirical best linear unbiased predictors are derived under the model. A parametric bootstrap procedure is proposed for the Estimation of the mean squared error of the Small Area estimators. The spatio-temporal model is compared with simpler models through simulation experiments, analyzing the gain in efficiency achieved by the use of the more complex model. The performance of the parametric bootstrap estimator of the mean squared error is also assessed. An application with Spanish EU-SILC data is carried out to obtain estimates of poverty indicators for Spanish provinces in 2008, making use of survey data from years 2004-2008.
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Small Area Estimation of poverty proportions under Area level time models
Computational Statistics & Data Analysis, 2012Co-Authors: Maria Dolores Esteban, Domingo Morales, Agustin Perez, L SantamariaAbstract:The unit-level Small Area Estimation approach has no standard procedure and each case needs separate modeling when the domain parameters are not linear or the target variable is not normally distributed. Area-level linear mixed models can be generally applied to produce EBLUP estimates of linear and non linear parameters because direct estimates are weighted sums, so that the assumption of normality may be acceptable. The problem of estimating Small Area non linear parameters is treated, with special emphasis on the Estimation of poverty proportions. Borrowing strength from time by using Area-level linear time models is proposed. Four time-dependent Area-level models are considered and the behavior of the two basic ones is empirically investigated. The developed model-based methodology for estimating poverty proportions is applied in the Spanish Living Conditions Survey.
Gauri Sankar Datta - One of the best experts on this subject based on the ideXlab platform.
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robust hierarchical bayes Small Area Estimation for the nested error linear regression model
International Statistical Review, 2019Co-Authors: Adrijo Chakraborty, Gauri Sankar Datta, Abhyuday MandalAbstract:Standard model‐based Small Area estimates perform poorly in presence of outliers. Sinha & Rao () 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 () 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 () 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.
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Estimation of crop yield distribution and insurance premium using shrinkage estimator a hierarchical bayes and Small Area Estimation approach
Research Papers in Economics, 2012Co-Authors: Sebastain Nde Awondo, Gauri Sankar Datta, Octavio A Ramirez, Esendugue Greg FonsahAbstract:Obtaining reliable estimates of insurance premiums is a critical step in risk sharing and risk transfer necessary to ensure solvency and continuity in crop insurance programs. Challenges encountered in the Estimation include dealing with aggregation bias from using county level yield averages as well as properly accounting for spatial and temporal heterogeneity. In this study, we associate some of these challenges as classical Small Area Estimation (SAE) problems. We employ a hierarchical Bayes (HB) SAE to obtain design consistent expected county level yields and Group Risk Plan (GRP) premiums for corm farms in Illinois using quasi-simulated data. Preliminary results show little bias (< 10%) in estimated expected county yields in several counties investigated. We found wide variation in GRP, APH and basis risk across counties for similar level of coverage and scale. Results show that farmers could lower their GRP premiums by as much as 30% by carefully choosing a coverage level and scale combination.
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bayesian benchmarking with applications to Small Area Estimation
Test, 2011Co-Authors: Malay Ghosh, Gauri Sankar Datta, Rebecca C Steorts, Jerry J MaplesAbstract:It is well-known that Small Area Estimation needs explicit or at least implicit use of models (cf. Rao in Small Area Estimation, Wiley, New York, 2003). These model-based estimates can differ widely from the direct estimates, especially for Areas with very low sample sizes. While model-based Small Area estimates are very useful, one potential difficulty with such estimates is that when aggregated, the overall estimate for a larger geographical Area may be quite different from the corresponding direct estimate, the latter being usually believed to be quite reliable. This is because the original survey was designed to achieve specified inferential accuracy at this higher level of aggregation. The problem can be more severe in the event of model failure as often there is no real check for validity of the assumed model. Moreover, an overall agreement with the direct estimates at an aggregate level may sometimes be politically necessary to convince the legislators of the utility of Small Area estimates. One way to avoid this problem is the so-called “benchmarking approach”, which amounts to modifying these model-based estimates so that we get the same aggregate estimate for the larger geographical Area. Currently, the most popular approach is the so-called “raking” or ratio adjustment method, which involves multiplying all the Small Area estimates by a constant data-dependent factor so that the weighted total agrees with the direct estimate. There are alternate proposals, mostly from frequentist considerations, which meet also the aforementioned benchmarking criterion. We propose in this paper a general class of constrained Bayes estimators which also achieve the necessary benchmarking. Many of the frequentist estimators, including some of the raked estimators, follow as special cases of our general result. Explicit Bayes estimators are derived which benchmark the weighted mean or both the weighted mean and weighted variability. We illustrate our methodology by developing poverty rates in school-aged children at the state level and then benchmarking these estimates to match at the national level. Unlike the existing frequentist benchmarking literature, which is primarily based on linear models, the proposed Bayesian approach can accommodate any arbitrary model, and the benchmarked Bayes estimators are based only on the posterior mean and the posterior variance-covariance matrix.
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model based approach to Small Area Estimation
Handbook of Statistics, 2009Co-Authors: Gauri Sankar DattaAbstract:Publisher Summary This chapter reviews both frequentist and Bayesian approaches to model based Small Area Estimation. Although the frequentist approach is still more popular among practitioners, the Bayesian approach is also gaining popularity and acceptability. The difficulty in the Bayesian approach is prior specification and computation. Although the former is still a difficult issue, enormous progress in recent years has been achieved on computational issues. It is worthwhile to point out that frequentist solutions based on jackknife or bootstrap are also computer intensive. One advantage with the Bayesian approach is that it automatically incorporates all sources of uncertainty associated with an inference problem. There are many more important applications of Small Area Estimation encountered by various government agencies. Indirect estimates of Small Area means that borrow strength from other Areas are referred to as cross-sectional estimates. On the other hand for a survey which is repeated regularly, one can obtain indirect estimates of Small Area means by borrowing strength both from other Areas and the time series.
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empirical best linear unbiased and empirical bayes prediction in multivariate Small Area Estimation
Journal of Statistical Planning and Inference, 1999Co-Authors: Gauri Sankar Datta, Bannmo Day, I V BasawaAbstract:Abstract Small Area Estimation plays a prominent role in survey sampling due to a growing demand for reliable Small Area estimates from both public and private sectors. Popularity of model-based inference is increasing in survey sampling, particularly, in Small Area Estimation. The estimates of the Small Area parameters can profitably ‘borrow strength’ from data on related multiple characteristics and/or auxiliary variables from other neighboring Areas through appropriate models. Fay (1987, Small Area Statistics, Wiley, New York, pp. 91–102) proposed multivariate regression for Small Area Estimation of multiple characteristics. The success of this modeling rests essentially on the strength of correlation of these dependent variables. To estimate Small Area mean vectors of multiple characteristics, multivariate modeling has been proposed in the literature via a multivariate variance components model. We use this approach to empirical best linear unbiased and empirical Bayes prediction of Small Area mean vectors. We use data from Battese et al. (1988, J. Amer. Statist. Assoc. 83, 28 –36) to conduct a simulation which shows that the multivariate approach may achieve substantial improvement over the usual univariate approach.
