IDEAS home Printed from https://ideas.repec.org/a/bla/jorssa/v181y2018i4p981-1008.html
   My bibliography  Save this article

Small area estimation under informative sampling and not missing at random non‐response

Author

Listed:
  • Michael Sverchkov
  • Danny Pfeffermann

Abstract

Pfeffermann and Sverchkov considered small area estimation for the case where the selection of the sampled areas is informative in the sense that the area sampling probabilities are related to the true (unknown) area means, and the sampling of units within the selected areas is likewise informative with probabilities that are related to the values of the study variable, in both cases after conditioning on the model covariates. We extend this approach to the practical situation of incomplete response at the unit level, and where the response is not missing at random. The proposed extension consists of first identifying the model holding for the observed responses and using the model for estimating the response probabilities, and then applying the approach of Pfeffermann and Sverchkov to the observed data with the unit sampling probabilities replaced by the products of the sampling probabilities and the estimated response probabilities. A bootstrap procedure for estimating the mean‐squared error of the proposed predictors is developed. We illustrate our approach by a simulation study and by application to a real data set. The simulations also illustrate the consequences of not accounting for informative sampling and/or non‐response.

Suggested Citation

  • Michael Sverchkov & Danny Pfeffermann, 2018. "Small area estimation under informative sampling and not missing at random non‐response," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 981-1008, October.
    • Handle: RePEc:bla:jorssa:v:181:y:2018:i:4:p:981-1008
    DOI: 10.1111/rssa.12362
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssa.12362
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssa.12362?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. Jae Kwang Kim & C. J. Skinner, 2013. "Weighting in survey analysis under informative sampling," Biometrika, Biometrika Trust, vol. 100(2), pages 385-398.
    2. Pfeffermann, Danny & Sverchkov, Michail, 2007. "Small-Area Estimation Under Informative Probability Sampling of Areas and Within the Selected Areas," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1427-1439, December.
    3. Danny Pfeffermann & Fernando Antonio Da Silva Moura & Pedro Luis Do Nascimento Silva, 2006. "Multi-level modelling under informative sampling," Biometrika, Biometrika Trust, vol. 93(4), pages 943-959, December.
    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. Nikos Tzavidis & Li‐Chun Zhang & Angela Luna & Timo Schmid & Natalia Rojas‐Perilla, 2018. "From start to finish: a framework for the production of small area official statistics," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 927-979, October.
    2. 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.
    3. Pfeffermann Danny & Ben-Hur Dano & Blum Olivia, 2019. "Planning The Next Census For Israel," Statistics in Transition New Series, Statistics Poland, vol. 20(1), pages 7-19, March.
    4. Peralta,Isabel Molina, 2024. "Frontiers in Small Area Estimation Research: Application to Welfare Indicators," Policy Research Working Paper Series 10828, The World Bank.
    5. Runge Marina & Schmid Timo, 2023. "Small Area with Multiply Imputed Survey Data," Journal of Official Statistics, Sciendo, vol. 39(4), pages 507-533, December.
    6. 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.
    7. Beręsewicz Maciej, 2019. "Correlates of Representation Errors in Internet Data Sources for Real Estate Market," Journal of Official Statistics, Sciendo, vol. 35(3), pages 509-529, September.
    8. Danny Pfeffermann & Dano Ben-Hur & Olivia Blum, 2019. "Planning The Next Census For Israel," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 7-19, March.

    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. A. Sikov & J. M. Stern, 2019. "Application of the full Bayesian significance test to model selection under informative sampling," Statistical Papers, Springer, vol. 60(1), pages 89-104, February.
    2. Elbers,Chris & Roy Van der Weide, 2025. "Non-Normal Empirical Bayes Prediction of Local Welfare," Policy Research Working Paper Series 11107, The World Bank.
    3. Maciej Beręsewicz & Dagmara Nikulin, 2018. "Informal employment in Poland: an empirical spatial analysis," Spatial Economic Analysis, Taylor & Francis Journals, vol. 13(3), pages 338-355, July.
    4. 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.
    5. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.
    6. repec:csb:stintr:v:17:y:2016:i:1:p:133-154 is not listed on IDEAS
    7. Abhishek Singh & Sabu Padmadas & Kaushalendra Kumar & Fiifi Amoako Johnson & Ashish Kumar Upadhyay & Ashish Singh, 2022. "Spatial heterogeneity in son preference across India’s 640 districts: An application of small-area estimation," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 47(26), pages 793-842.
    8. Michael A. Hidiroglou & Victor M. Estevao, 2016. "A Comparison Of Small Area And Calibration Estimators Via Simulation," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 133-154, March.
    9. Alexander Sun & Paul A. Parker & Scott H. Holan, 2022. "Analysis of Household Pulse Survey Public-Use Microdata via Unit-Level Models for Informative Sampling," Stats, MDPI, vol. 5(1), pages 1-15, February.
    10. Matthew R. Williams & Terrance D. Savitsky, 2021. "Uncertainty Estimation for Pseudo‐Bayesian Inference Under Complex Sampling," International Statistical Review, International Statistical Institute, vol. 89(1), pages 72-107, April.
    11. 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.
    12. Agne Bikauskaite & Isabel Molina & Domingo Morales, 2022. "Multivariate mixture model for small area estimation of poverty indicators," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S2), pages 724-755, December.
    13. Bor, Jacob & Venkataramani, Atheendar & Williams, David & Tsai, Alexander, 2024. "Reply to McCrain, Adams, Nix, and Del Pozo (2024), "Reconsidering a prominent finding on the spillover effects of police killings of unarmed Black Americans"," SocArXiv 6hx5p, Center for Open Science.
    14. Guadarrama, María & Molina, Isabel & Rao, J.N.K., 2018. "Small area estimation of general parameters under complex sampling designs," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 20-40.
    15. Oǧuz-Alper, Melike & Berger, Yves G., 2020. "Modelling multilevel data under complex sampling designs: An empirical likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    16. Swati Srivastava & Kaushalendra Kumar & Lotus McDougal & Ashish Kumar Upadhyay & Katherine Hay & Abhishek Singh, 2025. "Mapping women’s work in India: An application of small area estimation," PLOS ONE, Public Library of Science, vol. 20(2), pages 1-40, February.
    17. Hengfang Wang & Jae Kwang Kim, 2025. "Information projection approach to smoothed propensity score weighting for handling selection bias under missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(1), pages 127-153, February.
    18. J. N. K. Rao, 2021. "On Making Valid Inferences by Integrating Data from Surveys and Other Sources," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 242-272, May.
    19. Guadarrama, María & Molina, Isabel & Rao, J.N.K., 2016. "Small area estimation of general parameters under complex sampling designs," DES - Working Papers. Statistics and Econometrics. WS 22731, Universidad Carlos III de Madrid. Departamento de Estadística.
    20. Hidiroglou M. A. & Estevao V. M., 2016. "A Comparison of Small Area and Calibration Estimators Via Simulation," Statistics in Transition New Series, Statistics Poland, vol. 17(1), pages 133-154, March.
    21. Arnab Hazra & Pratik Nag & Rishikesh Yadav & Ying Sun, 2025. "Exploring the Efficacy of Statistical and Deep Learning Methods for Large Spatial Datasets: A Case Study," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 30(1), pages 231-254, 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:jorssa:v:181:y:2018:i:4:p:981-1008. 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: https://edirc.repec.org/data/rssssea.html .

    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.