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

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  • 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
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    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.
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    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. Pfeffermann Danny & Ben-Hur Dano & Blum Olivia, 2019. "Planning The Next Census For Israel," Statistics in Transition New Series, Polish Statistical Association, vol. 20(1), pages 7-19, March.
    3. 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.
    4. 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.
    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. 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.
    7. 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.

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