The Fay–Herriot Model in Small Area Estimation
Standard methods of variance component estimation used in the Fay-Herriot model for small areas can produce problems of inadmissible values (negative or zero) for these variances. This implies that the empirical best linear unbiased predictor of a small area mean does not take into account the vari...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Instituto Nacional de Estatística | Statistics Portugal
2020-10-01
|
| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/323 |
| _version_ | 1798039143858569216 |
|---|---|
| author | José Luis Ávila-Valdez Mauricio Huerta Víctor Leiva Marco Riquelme Leonardo Trujillo |
| author_facet | José Luis Ávila-Valdez Mauricio Huerta Víctor Leiva Marco Riquelme Leonardo Trujillo |
| author_sort | José Luis Ávila-Valdez |
| collection | DOAJ |
| description |
Standard methods of variance component estimation used in the Fay-Herriot model for small areas can produce problems of inadmissible values (negative or zero) for these variances. This implies that the empirical best linear unbiased predictor of a small area mean does not take into account the variance of the random effect of the corresponding area, reducing it to a regression estimator. In this paper, we propose an approach based on the expectation-maximization (EM) algorithm to solve the problem of inadmissibility. As stated in the theory of variance component estimation, we confirm through Monte Carlo simulations that the EM algorithm always produces strictly positive variance component estimates. In addition, we compare the performance of the proposed approach with two recently proposed methods in terms of relative bias, mean square error and mean square predictor error. We illustrate our approach with official data related to food security and poverty collected in Mexico, showing their potential applications.
|
| first_indexed | 2024-04-11T21:49:51Z |
| format | Article |
| id | doaj.art-dc109db058bb4f9aa38dac293d5a9db3 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-11T21:49:51Z |
| publishDate | 2020-10-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-dc109db058bb4f9aa38dac293d5a9db32022-12-22T04:01:17ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712020-10-0118510.57805/revstat.v18i5.323The Fay–Herriot Model in Small Area EstimationJosé Luis Ávila-Valdez 0Mauricio Huerta 1Víctor Leiva 2Marco Riquelme 3Leonardo Trujillo 4Universidad Popular Autónoma del Estado de PueblaUniversidad Católica de ValparaísoPontificia Universidad Católica de ValparaísoUniversidad de ValparaísoUniversidad Nacional de Colombia Standard methods of variance component estimation used in the Fay-Herriot model for small areas can produce problems of inadmissible values (negative or zero) for these variances. This implies that the empirical best linear unbiased predictor of a small area mean does not take into account the variance of the random effect of the corresponding area, reducing it to a regression estimator. In this paper, we propose an approach based on the expectation-maximization (EM) algorithm to solve the problem of inadmissibility. As stated in the theory of variance component estimation, we confirm through Monte Carlo simulations that the EM algorithm always produces strictly positive variance component estimates. In addition, we compare the performance of the proposed approach with two recently proposed methods in terms of relative bias, mean square error and mean square predictor error. We illustrate our approach with official data related to food security and poverty collected in Mexico, showing their potential applications. https://revstat.ine.pt/index.php/REVSTAT/article/view/323empirical best linear unbiased predictorfood security and povertyMonte Carlo simulationR softwarerandom effectsvariance components |
| spellingShingle | José Luis Ávila-Valdez Mauricio Huerta Víctor Leiva Marco Riquelme Leonardo Trujillo The Fay–Herriot Model in Small Area Estimation Revstat Statistical Journal empirical best linear unbiased predictor food security and poverty Monte Carlo simulation R software random effects variance components |
| title | The Fay–Herriot Model in Small Area Estimation |
| title_full | The Fay–Herriot Model in Small Area Estimation |
| title_fullStr | The Fay–Herriot Model in Small Area Estimation |
| title_full_unstemmed | The Fay–Herriot Model in Small Area Estimation |
| title_short | The Fay–Herriot Model in Small Area Estimation |
| title_sort | fay herriot model in small area estimation |
| topic | empirical best linear unbiased predictor food security and poverty Monte Carlo simulation R software random effects variance components |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/323 |
| work_keys_str_mv | AT joseluisavilavaldez thefayherriotmodelinsmallareaestimation AT mauriciohuerta thefayherriotmodelinsmallareaestimation AT victorleiva thefayherriotmodelinsmallareaestimation AT marcoriquelme thefayherriotmodelinsmallareaestimation AT leonardotrujillo thefayherriotmodelinsmallareaestimation AT joseluisavilavaldez fayherriotmodelinsmallareaestimation AT mauriciohuerta fayherriotmodelinsmallareaestimation AT victorleiva fayherriotmodelinsmallareaestimation AT marcoriquelme fayherriotmodelinsmallareaestimation AT leonardotrujillo fayherriotmodelinsmallareaestimation |