IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v49y2022i4p1699-1727.html
   My bibliography  Save this article

Empirical best prediction of small area bivariate parameters

Author

Listed:
  • María Dolores Esteban
  • María José Lombardía
  • Esther López‐Vizcaíno
  • Domingo Morales
  • Agustín Pérez

Abstract

This paper introduces empirical best predictors of small area bivariate parameters, like ratios of sums or sums of ratios, by assuming that the target unit‐level vector follows a bivariate nested error regression model. The corresponding means squared errors are estimated by parametric bootstrap. Several simulation experiments empirically study the behavior of the introduced statistical methodology. An application to real data from the Spanish household budget survey gives estimators of ratios of food household expenditures by provinces.

Suggested Citation

  • María Dolores Esteban & María José Lombardía & Esther López‐Vizcaíno & Domingo Morales & Agustín Pérez, 2022. "Empirical best prediction of small area bivariate parameters," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1699-1727, December.
    • Handle: RePEc:bla:scjsta:v:49:y:2022:i:4:p:1699-1727
    DOI: 10.1111/sjos.12618
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12618
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12618?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Monique Graf & J. Miguel Marín & Isabel Molina, 2019. "A generalized mixed model for skewed distributions applied to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 565-597, June.
    2. María Guadarrama & Isabel Molina & J. N. K. Rao, 2016. "A Comparison Of Small Area Estimation Methods For Poverty Mapping," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 41-66, March.
    3. Yolanda Marhuenda & Isabel Molina & Domingo Morales & J. N. K. Rao, 2017. "Poverty mapping in small areas under a twofold nested error regression model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1111-1136, October.
    4. Gonzalez-Manteiga, W. & Lombardia, M.J. & Molina, I. & Morales, D. & Santamaria, L., 2007. "Estimation of the mean squared error of predictors of small area linear parameters under a logistic mixed model," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2720-2733, February.
    5. Esther López-Vizcaíno & María José Lombardía & Domingo Morales, 2015. "Small area estimation of labour force indicators under a multinomial model with correlated time and area effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 535-565, June.
    6. repec:csb:stintr:v:17:y:2016:i:1:p:9-24 is not listed on IDEAS
    7. repec:csb:stintr:v:17:y:2016:i:1:p:41-66 is not listed on IDEAS
    8. J. L. Scealy & A. H. Welsh, 2017. "A Directional Mixed Effects Model for Compositional Expenditure Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 24-36, January.
    9. Roberto Benavent & Domingo Morales, 2021. "Small area estimation under a temporal bivariate area-level linear mixed model with independent time effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 195-222, March.
    10. Azka Ubaidillah & Khairil Anwar Notodiputro & Anang Kurnia & I. Wayan Mangku, 2019. "Multivariate Fay-Herriot models for small area estimation with application to household consumption per capita expenditure in Indonesia," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(15), pages 2845-2861, November.
    11. Tsubasa Ito & Tatsuya Kubokawa, 2021. "Empirical best linear unbiased predictors in multivariate nested-error regression models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(10), pages 2224-2249, May.
    12. Isabel Molina & Ayoub Saei & M. José Lombardía, 2007. "Small area estimates of labour force participation under a multinomial logit mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 975-1000, October.
    13. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2022. "Small area estimation of expenditure means and ratios under a unit-level bivariate linear mixed model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(1), pages 143-168, January.
    14. Stefano Marchetti & Luca Secondi, 2017. "Estimates of Household Consumption Expenditure at Provincial Level in Italy by Using Small Area Estimation Methods: “Real” Comparisons Using Purchasing Power Parities," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 131(1), pages 215-234, March.
    15. Andreea L. Erciulescu & Wayne A. Fuller, 2016. "Small Area Prediction Under Alternative Model Specifications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 9-24, March.
    16. Innocent Ngaruye & Joseph Nzabanita & Dietrich von Rosen & Martin Singull, 2017. "Small area estimation under a multivariate linear model for repeated measures data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(21), pages 10835-10850, November.
    17. Boubeta, Miguel & Lombardía, María José & Morales, Domingo, 2017. "Poisson mixed models for studying the poverty in small areas," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 32-47.
    18. Jiming Jiang & P. Lahiri, 2001. "Empirical Best Prediction for Small Area Inference with Binary Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 217-243, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. María Bugallo & Domingo Morales & María Dolores Esteban & Maria Chiara Pagliarella, 2024. "Model-Based Estimation of Small Area Dissimilarity Indexes: An Application to Sex Occupational Segregation in Spain," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 174(2), pages 473-501, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2023. "Small area estimation of average compositions under multivariate nested error regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 651-676, June.
    2. María Dolores Esteban & María José Lombardía & Esther López-Vizcaíno & Domingo Morales & Agustín Pérez, 2020. "Small area estimation of proportions under area-level compositional mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 793-818, September.
    3. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 65-96, February.
    4. Hao Sun & Emily Berg & Zhengyuan Zhu, 2022. "Bivariate small‐area estimation for binary and gaussian variables based on a conditionally specified model," Biometrics, The International Biometric Society, vol. 78(4), pages 1555-1565, December.
    5. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "$$\ell _2$$ ℓ 2 -penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 459-489, May.
    6. Angelo Moretti, 2023. "Estimation of small area proportions under a bivariate logistic mixed model," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(4), pages 3663-3684, August.
    7. Tomáš Hobza & Domingo Morales & Laureano Santamaría, 2018. "Small area estimation of poverty proportions under unit-level temporal binomial-logit mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 270-294, June.
    8. Guadarrama, María & Morales, Domingo & Molina, Isabel, 2021. "Time stable empirical best predictors under a unit-level model," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    9. Chandra, Hukum & Salvati, Nicola & Chambers, Ray, 2018. "Small area estimation under a spatially non-linear model," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 19-38.
    10. María Bugallo & Domingo Morales & María Dolores Esteban & Maria Chiara Pagliarella, 2024. "Model-Based Estimation of Small Area Dissimilarity Indexes: An Application to Sex Occupational Segregation in Spain," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 174(2), pages 473-501, September.
    11. Miguel Boubeta & María José Lombardía & Domingo Morales, 2016. "Empirical best prediction under area-level Poisson mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 548-569, September.
    12. Boubeta, Miguel & Lombardía, María José & Morales, Domingo, 2017. "Poisson mixed models for studying the poverty in small areas," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 32-47.
    13. Roberto Benavent & Domingo Morales, 2021. "Small area estimation under a temporal bivariate area-level linear mixed model with independent time effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 195-222, March.
    14. Merfeld,Joshua David & Newhouse,David Locke & Weber,Michael & Lahiri,Partha, 2022. "Combining Survey and Geospatial Data Can Significantly Improve Gender-DisaggregatedEstimates of Labor Market Outcomes," Policy Research Working Paper Series 10077, The World Bank.
    15. Isabel Molina & Paul Corral & Minh Nguyen, 2022. "Estimation of poverty and inequality in small areas: review and discussion," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1143-1166, December.
    16. Paul Walter & Marcus Groß & Timo Schmid & Nikos Tzavidis, 2021. "Domain prediction with grouped income data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1501-1523, October.
    17. Jan Pablo Burgard & Joscha Krause & Domingo Morales, 2022. "A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 204-234, March.
    18. M. Giovanna Ranalli & Giorgio E. Montanari & Cecilia Vicarelli, 2018. "Estimation of small area counts with the benchmarking property," METRON, Springer;Sapienza Università di Roma, vol. 76(3), pages 349-378, December.
    19. Isabel Molina & Ewa Strzalkowska‐Kominiak, 2020. "Estimation of proportions in small areas: application to the labour force using the Swiss Census Structural Survey," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(1), pages 281-310, January.
    20. Domingo Morales & Joscha Krause & Jan Pablo Burgard, 2022. "On the Use of Aggregate Survey Data for Estimating Regional Major Depressive Disorder Prevalence," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 344-368, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:scjsta:v:49:y:2022:i:4:p:1699-1727. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.