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A one-bring-one route for assessing the uncertainty of small area estimation in nested-error regression models

Author

Listed:
  • Yuzi Liu

    (Jiangxi University of Finance and Economics)

  • Haiqiang Ma

    (Jiangxi University of Finance and Economics)

  • Xiaohui Liu

    (Jiangxi University of Finance and Economics)

  • Jiming Jiang

    (University of California)

Abstract

The nested-error regression (NER) models are widely used to analyze unit-level data in small area estimation. Concerned about possible model misspecification, Jiang et al. (Surv Methodol 41:37–55, 2015) suggested a new prediction procedure, entitled observed best prediction (OBP), for the NER models and showed its desirable properties under such a setting. However, how to assess the uncertainty of OBP in such a case remains poorly addressed. This paper investigates this issue by developing a new estimator relying on the so-called one-bring-one route. It is shown that the new estimator is second-order unbiased under some mild conditions. Some simulations are conducted to confirm its finite sample performance. Finally, we applied the proposed estimator to a real-data example.

Suggested Citation

  • Yuzi Liu & Haiqiang Ma & Xiaohui Liu & Jiming Jiang, 2025. "A one-bring-one route for assessing the uncertainty of small area estimation in 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. 34(2), pages 383-430, June.
    • Handle: RePEc:spr:testjl:v:34:y:2025:i:2:d:10.1007_s11749-025-00965-x
    DOI: 10.1007/s11749-025-00965-x
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