Manifold regularization for small area estimation of domain proportions under informative sampling: Formulation, properties, simulation experiments

Joscha Krause

No 2026-11, Research Papers in Economics from University of Trier, Department of Economics

Abstract: Informative sampling refers to a regression model response being statistically related to sample inclusion even after conditioning on suitable covariates. The conditional response distribution inferred from the sample data may then differ from the true population distribution. If not accounted for, this can lead to biased or inaccurate estimates, especially on regional levels where domain observations are sparse. We study under which conditions manifold regularization improves domain estimation while adjusting for informative sampling. We combine a survey-weighted logit mixed model with a geometric penalty and residual correction for domain totals. Two settings are considered. In the first, covariates are observed for the total population, allowing the direct construction of the graph. In the second, covariates are only observed in an auxiliary probability sample, requiring estimation of the graph energy using second-order inclusion probabilities. For both settings, we derive exact conditions for reductions in squared design bias and mean squared error relative to the same weighted nonlinear model without geometric regularization. We also give sufficient conditions under which an improvement obtained with the population graph is preserved when the graph is estimated. Thereafter, we study the sensitivity towards informative sampling and show how to determine geometric penalty in practice. Design consistency and first-order interval validity support the proposed estimation procedure. A Monte Carlo study is conducted to assess these comparisons under different response surfaces and informative sampling mechanisms.

Keywords: bias correction; geometrical learning; model-assisted estimation; semi-supervised learning; survey weighting; uncertainty estimation (search for similar items in EconPapers)
Pages: 22 pages
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:trr:wpaper:202611

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