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

Yuzi Liu, Haiqiang Ma, Xiaohui Liu () and Jiming Jiang
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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

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2025, vol. 34, issue 2, No 3, 383-430

Abstract: 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.

Keywords: One-bring-one route; Uncertainty; Mean squared prediction error; Nested-error regression model; 62D99; 62F40 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11749-025-00965-x

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