Small area estimation when auxiliary information is measured with error

Ybarra, Lynn M. R.; Lohr, Sharon L.

doi:10.1093/biomet/asn048

Cited by 108 publications

(157 citation statements)

References 6 publications

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“…Now, if we substituteX i for X i in (2.2), then the resulting substitution predictor,θ iS , is worse thanθ iF H in the sense of the mean squared prediction error (MSPE). Moreover, if b T C i b > σ 2 ν + ψ i , then usingθ iS is worse than using the direct estimator (Ybarra and Lohr, 2008). Now following the idea given in Datta et al (2010) we obtain a pseudo-Bayes predictor of θ i by estimating X i efficiently.…”

Section: Empirical Bayes Estimationmentioning

confidence: 99%

“…where Ybarra and Lohr (2008) obtained the minimum MSPE predictor,θ iM E , among all linear combination of y i andX T i b of the form of a i y i + (1 − a i )X T i b. It turns out that the Ybarra-Lohr predictorθ iM E is the same as the pseudo-Bayes predictorθ iP B .…”

Section: Empirical Bayes Estimationmentioning

confidence: 99%

“…Bolfarine et al (1996) and Goo and Kim (2012) studied measurement error regression models in finite population sampling. Ghosh et al (2006), Ghosh and Sinha (2007), Torabi et al (2010), Datta et al (2010), and Ybarra and Lohr (2008) considered small area models with covariates subject to measurement error.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian small area estimations with measurement errors

Goo¹,

Kim

2013

Journal of the Korean Data and Information Science Society

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This paper considers Bayes estimations of the small area means under Fay-Herriot model with measurement errors. We provide empirical Bayes predictors of small area means with the corresponding jackknifed mean squared prediction errors. Also we obtain hierarchical Bayes predictors and the corresponding posterior standard deviations using Gibbs sampling. Numerical studies are provided to illustrate our methods and compare their efficiencies.

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Section: Empirical Bayes Estimationmentioning

confidence: 99%

Section: Empirical Bayes Estimationmentioning

confidence: 99%

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Bayesian small area estimations with measurement errors

Goo¹,

Kim

2013

Journal of the Korean Data and Information Science Society

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“…To produce more reliable estimators at the small area level, a common approach is to use model-based methods which combine data from multiple sources, surveys, administrative records, registers and social media; see for example Rao (2003), Pfeffermann (2013), Ybarra and Lohr (2008) and Rao and Molina (2015). Suppose we are interested in predicting a random quantity T j in small area j, where j = 1, .…”

Section: Introductionmentioning

confidence: 99%

“…A difficulty in applications is that it is not always possible to measure all the components of the auxiliary vectors A j accurately, and the techniques developed for covariates without measurement error may perform rather poorly in this case; see for example, Ghosh et al (2006), Ybarra and Lohr (2008) and Torabi et al (2009). In particular, if the measurement error is not taken into account, using the auxiliary A j s may result in estimators that are even less accurate than those based on the direct data from the small areas; see Ybarra and Lohr (2008), who propose a corrected small area predictor based on the empirical best linear unbiased prediction approach.…”

Section: Introductionmentioning

confidence: 99%

Semi-parametric prediction intervals in small areas when auxiliary data are measured with error.

Datta¹,

Delaigle²,

Hall³

et al. 2018

STAT SINICA

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In recent years, demand for reliable small area statistics has considerably increased, but the size of samples obtained in small areas is too often small to produce accurate predictors of quantities of interest. To overcome this difficulty, a common approach is to use auxiliary data from other areas or other sources, and produce estimators that combine them with direct data. A popular model for combining direct and indirect data sources is the Fay-Herriot model, which assumes that the auxiliary variables are observed accurately. However, these variables are often subject to measurement errors, and not taking this into account can lead to estimators that are even worse than those based exclusively on the direct data. In this paper, we consider structural measurement error models and a semi-parametric approach based on the Fay-Herriot model to produce reliable prediction intervals for small area characteristics of interest. Our theoretical study reveals the surprising fact that the properties of the prediction interval are not the same for all values of the noisy covariate. Indeed, the convergence rates are slower when the contaminated covariate takes the value zero than in other cases. Our procedure is illustrated with an application and simulation studies. Foreword: Our friend and colleague Peter Hall died in Melbourne, Australia on January 9, 2016, before this manuscript was completed. Peter worked hard on this paper before he fell ill, deriving all the theoretical results of the manuscript, whence our decision to submit this manuscript for the special issue in his honour. His theory is particularly striking since it reveals that the properties of the prediction interval depend on whether or not the contaminated covariate takes the value zero. Peter was very interested by this phenomenon but could not find an intuitive explanation to it. We checked his proofs thoroughly but could not find an intuitive explanation either, except that a similar behaviour is sometimes encountered in other problems.Abstract: In recent years, demand for reliable small area statistics has considerably increased, but the size of samples obtained in small areas is too often small to produce accurate predictors of quantities of interest. To overcome this difficulty, a common approach is to use auxiliary data from other areas or other sources, and produce estimators that combine them with direct data. A popular model for combining direct and indirect data sources is the Fay-Herriot model, which assumes that the auxiliary variables are observed accurately. However, these variables are often subject to measurement errors, and not taking this into account can lead to estimators that are even worse than those based exclusively on the direct data. We consider structural measurement error models and a semi-parametric approach based on the Fay-Herriot model to produce reliable prediction intervals for small area characteristics of interest. Our theoretical study reveals the surprising fact that the properties of the prediction interval are not ...

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2015

Small Area Estimation

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Small area estimation when auxiliary information is measured with error

Cited by 108 publications

References 6 publications

Bayesian small area estimations with measurement errors

Bayesian small area estimations with measurement errors

Semi-parametric prediction intervals in small areas when auxiliary data are measured with error.

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