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Direct domain estimation via regression-tree-assisted est...
[Submitted on 6 Jun 2026] · 2026-06-09 · via stat updates on arXiv.org

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Abstract:National statistical offices (NSOs) produce their estimates under a single weighting system (uni-weight approach): one set of weights, independent of the variable of interest, is used to estimate multiple parameters and multiple subpopulations (domains). In this paper we study, within the family of model-assisted estimators and from a design-based perspective of direct estimation, the use of regression trees as the assisting model for estimating totals in unplanned domains. We distinguish two strategies: (i) fitting a single tree at the population level and deriving from it uni-weight weights applicable to any domain, and fitting a domain-specific tree. We show that both estimators can be written as weighted sums with weights that do not depend on $y$, preserving the uni-weight property and additivity benchmarking with respect to the population total. Extending to trees the classical result, we argue why the estimator built from a population-level model tends to behave like the Horvitz-Thompson estimator within domains, whereas the domain-specific model can achieve substantial variance reductions. A simulation study based on microdata from the Uruguayan Continuous Household Survey (ECH) illustrates the behavior of the estimators at the population level and by department

Submission history

From: Juan Pablo Ferreira-Neira [view email]
[v1] Sat, 6 Jun 2026 18:20:26 UTC (397 KB)