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Esteban MD, Lombardía MJ, López-Vizcaíno E, Morales D, Pérez A. Small area estimation of average compositions under multivariate nested error regression models. TEST-SPAIN 2023. [DOI: 10.1007/s11749-023-00847-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/23/2023]
Abstract
AbstractThis paper investigates the small area estimation of population averages of unit-level compositional data. The new methodology transforms the compositions into vectors of $$R^m$$
R
m
and assumes that the vectors follow a multivariate nested error regression model. Empirical best predictors of domain indicators are derived from the fitted model, and their mean squared errors are estimated by parametric bootstrap. The empirical analysis of the behavior of the introduced predictors is investigated by means of simulation experiments. An application to real data from the Spanish household budget survey is given. The target is to estimate the average of proportions of annual household expenditures on food, housing and others, by Spanish provinces.
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A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates. TEST-SPAIN 2022. [DOI: 10.1007/s11749-021-00776-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
AbstractThe 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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Krause J, Burgard JP, Morales D. Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model. STAT NEERL 2021. [DOI: 10.1111/stan.12253] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Joscha Krause
- Department of Economic and Social Statistics Trier University Trier Germany
| | - Jan Pablo Burgard
- Department of Economic and Social Statistics Trier University Trier Germany
| | - Domingo Morales
- Operations Research Center University Miguel Hernández de Elche Elche Spain
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