Evidence
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The reviewed literature indicates that linkage error and model misspecification remain central concerns in data integration, and that robust and semi-parametric approaches have been developed to address them. Extending such methods to the big-data-assisted small area estimation settings discussed here, together with reliable mean squared error estimation, remains an open direction for future research.
Passages supplied to the Evidence version
Card 1 · Small Area Estimation with Linked Data
In Small Area Estimation data linkage can be used to combine values of the variableof interest from a national survey with values of auxiliary variables obtained from another source like a population register. Linkage errors can induce bias when fitting regression models; moreover, they can create n…
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In Small Area Estimation data linkage can be used to combine values of the variableof interest from a national survey with values of auxiliary variables obtained from another source like a population register. Linkage errors can induce bias when fitting regression models; moreover, they can create non-representative outliers in the linked data in addition to the presence of potential representative outliers. In this paper we adopt a secondary analyst's point view, assuming limited information is available on the linkage process, and we develop small area estimators based on linear mixed and linear M-quantile models to accommodate linked data containing a mix of both types of outliers. We illustrate the properties of these small area estimators, as well as estimators of their mean squared error, by means of model-based and design-based simulation experiments. These experiments show that the proposed predictors can lead to more efficient estimators when there is linkage error. Furthermor …
Card 2 · Robust Empirical Bayes Small Area Estimation with Density Power Divergence
A two-stage normal hierarchical model called the Fay--Herriot model and the empirical Bayes estimator are widely used to provide indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator might be poor when the assumed normal distribution is…
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A two-stage normal hierarchical model called the Fay--Herriot model and the empirical Bayes estimator are widely used to provide indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator might be poor when the assumed normal distribution is misspecified. In this article, we propose a simple modification by using density power divergence and suggest a new robust empirical Bayes small area estimator. The mean squared error and estimated mean squared error of the proposed estimator are derived based on the asymptotic properties of the robust estimator of the model parameters. We investigate the numerical performance of the proposed method through simulations and an application to survey data.
Card 3 · Nonnegative mean squared prediction error estimation in small area estimation
Small area estimation has received enormous attention in recent years due to its wide range of application, particularly in policy making decisions. The variance based on direct sample size of small area estimator is unduly large and there is a need of constructing model based estimator with low mea…
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Small area estimation has received enormous attention in recent years due to its wide range of application, particularly in policy making decisions. The variance based on direct sample size of small area estimator is unduly large and there is a need of constructing model based estimator with low mean squared prediction error (MSPE). Estimation of MSPE and in particular the bias correction of MSPE plays the central piece of small area estimation research. In this article, a new technique of bias correction for the estimated MSPE is proposed. It is shown that that the new MSPE estimator attains the same level of bias correction as the existing estimators based on straight Taylor expansion and jackknife methods. However, unlike the existing methods, the proposed estimate of MSPE is always nonnegative. Furthermore, the proposed method can be used for general two-level small area models where the variables at each level can be discrete or continuous and, in particular, be nonnormal.
Card 4 · Semiparametric empirical best prediction for small area estimation of unemployment indicators
The Italian National Institute for Statistics regularly provides estimates of unemployment indicators using data from the labor force survey. However, direct estimates of unemployment incidence cannot be released for local labor market areas. These are unplanned domains defined as clusters of munici…
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The Italian National Institute for Statistics regularly provides estimates of unemployment indicators using data from the labor force survey. However, direct estimates of unemployment incidence cannot be released for local labor market areas. These are unplanned domains defined as clusters of municipalities; many are out-of-sample areas, and the majority is characterized by a small sample size which renders direct estimates inadequate. The empirical best predictor represents an appropriate, model-based alternative. However, for non-Gaussian responses its computation and the computation of the analytic approximation to its mean squared error require the solution of (possibly) multiple integrals that, generally, have not a closed form. To solve the issue, Monte Carlo methods and parametric bootstrap are common choices, even though the computational burden is a nontrivial task. In this paper, we propose a semiparametric empirical best predictor for a (possibly) nonlinear mixed effect mode …
Card 5 · A Bayesian semi-parametric model for small area estimation
<!-- *** Custom HTML *** --> In public health management there is a need to produce subnational estimates of health outcomes. Often, however, funds are not available to collect samples large enough to produce traditional survey sample estimates for each subnational area. Although parametric hierarch…
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<!-- *** Custom HTML *** --> In public health management there is a need to produce subnational estimates of health outcomes. Often, however, funds are not available to collect samples large enough to produce traditional survey sample estimates for each subnational area. Although parametric hierarchical methods have been successfully used to derive estimates from small samples, there is a concern that the geographic diversity of the U.S. population may be oversimplified in these models. In this paper, a semi-parametric model is used to describe the geographic variability component of the model. Specifically, we assume Dirichlet process mixtures of normals for county-specific random effects. Results are compared to a parametric model based on the base measure of the Dirichlet process, using binary health outcomes related to mammogram usage.
Model-reported card use
Card 1 · fact
Affected output: linkage error and model misspecification remain central concerns in data integration
Model explanation: This row supplied the concrete linkage-error concern that anchors the first clause of the concluding synthesis.
Card 2 · fact
Affected output: model misspecification remain central concerns in data integration
Model explanation: This row supplied the misspecification concern that pairs with linkage error in the synthesis.
Card 4 · fact
Affected output: robust and semi-parametric approaches have been developed to address them
Model explanation: This row supplied the semi-parametric approach that the synthesis names as a response to these concerns.