On cross-validation for small area estimators

Fuente: arXiv
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Main Authors: Dong, Qianyu, Li, Zehang Richard
Format: Preprint
Published: 2026
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author Dong, Qianyu
Li, Zehang Richard
author_facet Dong, Qianyu
Li, Zehang Richard
contents Subnational monitoring of public health often relies on household surveys where data are sparse at the desired spatial resolution. Small area estimation (SAE) methods address this challenge by borrowing strength across areas and incorporating auxiliary information. However, comparing these estimators remains difficult in the absence of ground truth. We propose a cross-validation framework for evaluating small area estimators that accommodates complex survey designs. Our approach enables model-agnostic comparisons between area-level and unit-level SAE models. Central to our framework is a decomposition of the cross-validated squared error, which reveals both identifiable bias and unidentifiable components that can be bounded. Our theoretical results and simulation studies show that conventional approaches, such as leave-one-area-out cross-validation, can yield misleading model rankings, whereas the proposed approach offers more robust and interpretable model comparison with uncertainty quantification. We demonstrate the framework through a case study comparing SAE models estimating the subnational female literacy rate using Demographic and Health Surveys from Zambia.
format Preprint
id arxiv_https___arxiv_org_abs_2604_23464
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On cross-validation for small area estimators
Dong, Qianyu
Li, Zehang Richard
Methodology
Applications
Subnational monitoring of public health often relies on household surveys where data are sparse at the desired spatial resolution. Small area estimation (SAE) methods address this challenge by borrowing strength across areas and incorporating auxiliary information. However, comparing these estimators remains difficult in the absence of ground truth. We propose a cross-validation framework for evaluating small area estimators that accommodates complex survey designs. Our approach enables model-agnostic comparisons between area-level and unit-level SAE models. Central to our framework is a decomposition of the cross-validated squared error, which reveals both identifiable bias and unidentifiable components that can be bounded. Our theoretical results and simulation studies show that conventional approaches, such as leave-one-area-out cross-validation, can yield misleading model rankings, whereas the proposed approach offers more robust and interpretable model comparison with uncertainty quantification. We demonstrate the framework through a case study comparing SAE models estimating the subnational female literacy rate using Demographic and Health Surveys from Zambia.
title On cross-validation for small area estimators
topic Methodology
Applications
url https://arxiv.org/abs/2604.23464