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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
On Data Thinning for Model Validation in Small Area Estim...
Sho Kawano, Paul A. Parker, Zehang Richard Li · 2026-04-05 · via stat updates on arXiv.org

Small area estimation (SAE) produces estimates of population parameters for geographic and demographic subgroups with limited sample sizes. Such estimates are critical for informing policy decisions, ranging from poverty mapping to social program funding. Despite its widespread use, principled validation of SAE models remains challenging and general guidelines are far from well-established. Unlike conventional predictive modeling settings, validation data are rarely available in the SAE context. External validation surveys or censuses often do not exist, and access to individual-level microdata is often restricted, making standard cross-validation infeasible. In this paper, we propose a novel model validation scheme using only area-level direct survey estimates under the widely used Fay-Herriot model. Our approach is based on data thinning, which splits area-level observations into independent training and test components to enable out-of-sample validation. Our theoretical analysis reveals a fundamental tension inherent in thinning-based validation: performance metrics measured on the thinned training component target a different quantity than those based on the full data, with the gap varying by model complexity. Increasing the information allocated for training reduces this gap but inflates the variance of the estimator. We formally characterize this bias-variance tradeoff and provide practical recommendations for the thinning parameters that balance these competing considerations for model comparison. We show that data thinning with these settings provides consistent and stable performance across heterogeneous sampling designs in design-based simulations using American Community Survey microdata.