A Fay–Herriot model when auxiliary variables are measured with error

Burgard, Jan Pablo; Esteban, Maria J.; Morales, Domingo; Pérez, Agustín

doi:10.1007/s11749-019-00649-3

Cited by 21 publications

(18 citation statements)

References 18 publications

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“…The principle is repeated until all domain-specific subsamples have been deleted once. With this resampling scheme, we obtain an approximation to the prediction uncertainty resulting from model parameter estimation (Jiang et al 2002;Burgard et al 2020a). The deviation of the produced predictions from the original predictions based on all sample observations are quantified.…”

Section: Conservative Jacknife Estimatormentioning

confidence: 99%

The generalized equivalence of regularization and min–max robustification in linear mixed models

et al. 2021

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The connection between regularization and min–max robustification in the presence of unobservable covariate measurement errors in linear mixed models is addressed. We prove that regularized model parameter estimation is equivalent to robust loss minimization under a min–max approach. On the example of the LASSO, Ridge regression, and the Elastic Net, we derive uncertainty sets that characterize the feasible noise that can be added to a given estimation problem. These sets allow us to determine measurement error bounds without distribution assumptions. A conservative Jackknife estimator of the mean squared error in this setting is proposed. We further derive conditions under which min-max robust estimation of model parameters is consistent. The theoretical findings are supported by a Monte Carlo simulation study under multiple measurement error scenarios.

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Section: Conservative Jacknife Estimatormentioning

confidence: 99%

The generalized equivalence of regularization and min–max robustification in linear mixed models

et al. 2021

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“…. , T , then μ ebp d is equivalent to the EBP under the measurement error Fay-Herriot model studied by Ybarra and Lohr (2008) as well as Burgard et al (2020a).…”

Section: Empirical Best Predictionmentioning

confidence: 99%

“…The basic idea of these methods is to introduce distribution assumptions on the errors and make statistical inference under this premise. On that note, Ybarra and Lohr (2008), Burgard et al (2020a) and Burgard et al (2021) provided extensions of the area-level model that explicitly account for explanatory variable errors. A related approach was developed by Torabi et al (2009) for unit-level observations.…”

Section: Introductionmentioning

confidence: 99%

A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates

Burgard

Krause

Morales

2021

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The assessment of prevalence on regional levels is an important element of public health reporting. Since regional prevalence is rarely collected in registers, corresponding figures are often estimated via small area estimation using suitable health data. However, such data are frequently subject to uncertainty as values have been estimated from surveys. In that case, the method for prevalence estimation must explicitly account for data uncertainty to allow for reliable results. This can be achieved via measurement error models that introduce distribution assumptions on the noisy data. However, these methods usually require target and explanatory variable errors to be independent. This does not hold when data for both have been estimated from the same survey, which is sometimes the case in official statistics. If not accounted for, prevalence estimates can be severely biased. We propose a new measurement error model for regional prevalence estimation that is suitable for settings where target and explanatory variable errors are dependent. We derive empirical best predictors and demonstrate mean-squared error estimation. A maximum likelihood approach for model parameter estimation is presented. Simulation experiments are conducted to prove the effectiveness of the method. An application to regional hypertension prevalence estimation in Germany is provided.

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“…where B ¼ diag MEBFH model can be considered as a multivariate generalization of the Fay-Herriot model with measurement error studied by Ybarra and Lohr (2008) or by Burgard et al (2019). This approach was also considered by Arima et al (2017)…”

Section: The Measurement Error Bivariate Fay-herriot Modelmentioning

confidence: 99%

“…This last work was later extended by Arima et al (2017) proposing multivariate Fay-Herriot Bayesian predictors of small area means under functional measurement error. On the other hand, Burgard et al (2019) followed a likelihood-based approach for extending the Ybarra-Lohr model. They proposed residual maximum likelihood (REML) estimators of the model parameters and introduced empirical best predictors and a mean squared error analytical approximation.…”

Section: Introductionmentioning

confidence: 99%

Small area estimation under a measurement error bivariate Fay–Herriot model

et al. 2020

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The bivariate Fay-Herriot model is an area-level linear mixed model that can be used for estimating the domain means of two correlated target variables. Under this model, the dependent variables are direct estimators calculated from survey data and the auxiliary variables are true domain means obtained from external data sources. Administrative registers do not always give good auxiliary variables, so that statisticians sometimes take them from alternative surveys and therefore they are measured with error. We introduce a variant of the bivariate Fay-Herriot model that takes into account the measurement error of the auxiliary variables and we give fitting algorithms to estimate the model parameters. Based on the new model, we introduce empirical best predictors of domain means and we propose a parametric bootstrap procedure for estimating the mean squared error. We finally give an application to estimate poverty proportions and gaps in the Spanish Living Condition Survey, with auxiliary information from the Spanish Labour Force Survey.

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A Fay–Herriot model when auxiliary variables are measured with error

Cited by 21 publications

References 18 publications

The generalized equivalence of regularization and min–max robustification in linear mixed models

The generalized equivalence of regularization and min–max robustification in linear mixed models

A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates

Small area estimation under a measurement error bivariate Fay–Herriot model

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