IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i10p2889-2902.html
   My bibliography  Save this article

Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators

Author

Listed:
  • Marchetti, Stefano
  • Tzavidis, Nikos
  • Pratesi, Monica

Abstract

Small area estimation is conventionally concerned with the estimation of small area averages and totals. More recently emphasis has been also placed on the estimation of poverty indicators and of key quantiles of the small area distribution function using robust models, for example, the M-quantile small area model. In parallel to point estimation, Mean Squared Error (MSE) estimation is an equally crucial and challenging task. However, while analytic MSE estimation for small area averages is possible, analytic MSE estimation for quantiles and poverty indicators is difficult. Moreover, one of the main criticisms of the analytic MSE estimator for M-quantile estimates of small area averages is that it can be unstable when the area-specific sample sizes are small. A non-parametric bootstrap framework for MSE estimation for small area averages, quantiles and poverty indicators estimated with the M-quantile small area model is proposed. Emphasis is placed on second order properties of MSE estimators with results suggesting that the bootstrap MSE estimator is more stable than corresponding analytic MSE estimators. The proposed bootstrap is evaluated in a series of simulation studies under different parametric assumptions for the model error terms and different scenarios for the area-specific sample and population sizes. Finally, results from the application of the proposed MSE estimator to real income data from the European Survey of Income and Living Conditions (EU-SILC) in Italy are presented and information on the availability of R functions that can be used for implementing the proposed estimation procedures in practice is provided.

Suggested Citation

  • Marchetti, Stefano & Tzavidis, Nikos & Pratesi, Monica, 2012. "Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2889-2902.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:10:p:2889-2902
    DOI: 10.1016/j.csda.2012.01.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312000631
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.01.023?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    2. Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-766, May.
    3. Ray Chambers & Nikos Tzavidis, 2006. "M-quantile models for small area estimation," Biometrika, Biometrika Trust, vol. 93(2), pages 255-268, June.
    4. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    7. Kokic, Philip, et al, 1997. "A Measure of Production Performance," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 445-451, October.
    8. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    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. Domingo Morales & María del Mar Rueda & Dolores Esteban, 2018. "Model-Assisted Estimation of Small Area Poverty Measures: An Application within the Valencia Region in Spain," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(3), pages 873-900, August.
    2. Bilton, Penny & Jones, Geoff & Ganesh, Siva & Haslett, Steve, 2017. "Classification trees for poverty mapping," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 53-66.
    3. Francesco Schirripa Spagnolo & Antonella D’Agostino & Nicola Salvati, 2018. "Measuring differences in economic standard of living between immigrant communities in Italy," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1643-1667, July.
    4. 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.
    5. Hongjian Yu & Yueyan Wang & Jean Opsomer & Pan Wang & Ninez A. Ponce, 2018. "A design‐based approach to small area estimation using a semiparametric generalized linear mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1151-1167, October.
    6. Imam, M. F. & Islam, Mohammad Amirul & Alam, M. A. & Hossain, M. Jamal. & Das, Sumonkanti, 2020. "Small Area Estimation Of Poverty In Rural Bangladesh," Bangladesh Journal of Agricultural Economics, Bangladesh Agricultural University, vol. 40(1&2), February.
    7. Marchetti Stefano & Tzavidis Nikos, 2021. "Robust Estimation of the Theil Index and the Gini Coeffient for Small Areas," Journal of Official Statistics, Sciendo, vol. 37(4), pages 955-979, December.
    8. 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.
    9. Angelo Moretti & Natalie Shlomo & Joseph W. Sakshaug, 2021. "Small Area Estimation of Latent Economic Well-being," Sociological Methods & Research, , vol. 50(4), pages 1660-1693, November.
    10. Penelope Bilton & Geoff Jones & Siva Ganesh & Stephen Haslett, 2020. "Regression trees for poverty mapping," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(4), pages 426-443, December.
    11. Marchetti Stefano & Giusti Caterina & Pratesi Monica & Salvati Nicola & Giannotti Fosca & Pedreschi Dino & Rinzivillo Salvatore & Pappalardo Luca & Gabrielli Lorenzo, 2015. "Small Area Model-Based Estimators Using Big Data Sources," Journal of Official Statistics, Sciendo, vol. 31(2), pages 263-281, June.
    12. Stefano Marchetti & Maciej Beręsewicz & Nicola Salvati & Marcin Szymkowiak & Łukasz Wawrowski, 2018. "The use of a three‐level M‐quantile model to map poverty at local administrative unit 1 in Poland," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1077-1104, October.
    13. 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.
    14. Angelo Moretti & Natalie Shlomo & Joseph W. Sakshaug, 2020. "Multivariate Small Area Estimation of Multidimensional Latent Economic Well‐being Indicators," International Statistical Review, International Statistical Institute, vol. 88(1), pages 1-28, April.
    15. Stefano Marchetti & Caterina Giusti & Nicola Salvati & Monica Pratesi, 2017. "Small area estimation based on M-quantile models in presence of outliers in auxiliary variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 531-555, November.
    16. Zhang, Xingmin & Zhang, Shuai, 2021. "Optimal time-varying tail risk network with a rolling window approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).

    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. N. Salvati & N. Tzavidis & M. Pratesi & R. Chambers, 2012. "Small area estimation via M-quantile geographically weighted regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 1-28, March.
    2. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    3. G. Bertarelli & R. Chambers & N. Salvati, 2021. "Outlier robust small domain estimation via bias correction and robust bootstrapping," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 331-357, March.
    4. Giulia Romano & Nicola Salvati & Andrea Guerrini, 2014. "Factors Affecting Water Utility Companies’ Decision to Promote the Reduction of Household Water Consumption," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(15), pages 5491-5505, December.
    5. Stefano Marchetti & Caterina Giusti & Nicola Salvati & Monica Pratesi, 2017. "Small area estimation based on M-quantile models in presence of outliers in auxiliary variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 531-555, November.
    6. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    7. De Novellis, G. & Musile Tanzi, P. & Ranalli, M.G. & Stanghellini, E., 2024. "Leveraged finance exposure in the banking system: Systemic risk and interconnectedness," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 90(C).
    8. Walter, Paul & Groß, Markus & Schmid, Timo & Tzavidis, Nikos, 2017. "Estimation of linear and non-linear indicators using interval censored income data," Discussion Papers 2017/22, Free University Berlin, School of Business & Economics.
    9. Daouia, Abdelaati & Padoan, Simone A. & Stupfler, Gilles, 2023. "Extreme expectile estimation for short-tailed data, with an application to market risk assessment," TSE Working Papers 23-1414, Toulouse School of Economics (TSE), revised May 2024.
    10. Christophe Muller & Sami Bibi, 2006. "Focused Targeting against Poverty Evidence from Tunisia," IDEP Working Papers 0602, Institut d'economie publique (IDEP), Marseille, France, revised Apr 2006.
    11. Francesco Schirripa Spagnolo & Nicola Salvati & Antonella D’Agostino & Ides Nicaise, 2020. "The use of sampling weights in M‐quantile random‐effects regression: an application to Programme for International Student Assessment mathematics scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 991-1012, August.
    12. Abdelaati Daouia & Irène Gijbels & Gilles Stupfler, 2022. "Extremile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1579-1586, September.
    13. Nikos Tzavidis & Nicola Salvati & Monica Pratesi & Ray Chambers, 2008. "M-quantile models with application to poverty mapping," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 393-411, July.
    14. Abdelaati Daouia & Gilles Stupfler, 2024. "Extremile Regression," Post-Print hal-04697061, HAL.
    15. Christophe MULLER & Sami BIBI, 2008. "Focused Transfer Targeting against Poverty Evidence from Tunisia," THEMA Working Papers 2008-37, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    16. Brown, Caitlin & Ravallion, Martin & van de Walle, Dominique, 2018. "A poor means test? Econometric targeting in Africa," Journal of Development Economics, Elsevier, vol. 134(C), pages 109-124.
    17. G. De Novellis & M. Doretti & G. E. Montanari & M. G. Ranalli & N. Salvati, 2024. "Performance evaluation of nursing homes using finite mixtures of logistic models and M-quantile regression for binary data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(3), pages 753-781, July.
    18. Stefano Marchetti & Maciej Beręsewicz & Nicola Salvati & Marcin Szymkowiak & Łukasz Wawrowski, 2018. "The use of a three‐level M‐quantile model to map poverty at local administrative unit 1 in Poland," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1077-1104, October.
    19. Abdelaati Daouia & Simone A. Padoan & Gilles Stupfler, 2024. "Extreme expectile estimation for short-tailed data," Post-Print hal-04672516, HAL.
    20. Enrico Fabrizi & Caterina Giusti & Nicola Salvati & Nikos Tzavidis, 2014. "Mapping average equivalized income using robust small area methods," Papers in Regional Science, Wiley Blackwell, vol. 93(3), pages 685-701, August.

    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:eee:csdana:v:56:y:2012:i:10:p:2889-2902. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.