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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
Robust Likelihood Ratio Tests for Incomplete Economic Models
[Submitted on 10 Oct 2019 (v1), last revised 3 Jul 2026 (this ve · 2019-10-10 · via stat updates on arXiv.org

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Abstract:Economic models with multiple equilibria, self-selection, or weak behavioral restrictions often make set-valued predictions and therefore do not imply a unique likelihood. This paper develops robust likelihood-ratio tests for structural hypotheses in such incomplete models. We evaluate tests by their power guarantee, defined as the smallest rejection probability over all selection mechanisms compatible with the alternative, while requiring uniform size control over all null selections. Using the Huber--Strassen theory of least favorable pairs, we construct finite-sample minimax likelihood-ratio tests. The main result shows that, in repeated experiments, the least favorable pair is the product of the single-experiment least favorable pairs whenever the latent variables are independent across experiments. This product structure holds even though unrestricted selection may induce arbitrary heterogeneity and dependence in the observed outcomes. It reduces a high-dimensional robust testing problem to single-experiment calculations and yields exact finite-sample critical values and Gaussian approximations. For directed one-sided alternatives, we provide conditions under which conditioning on a selection-invariant statistic delivers exact conditional uniformly most powerful (UMP) tests with respect to the power guarantee. In the examples, these optimal tests are simple and interpretable, using selection-invariant features of the data that are directly tied to the hypothesis of interest. Monte Carlo experiments in entry-game and Roy-model designs illustrate size control, power, and the role of robust testability.

Submission history

From: Hiroaki Kaido [view email]
[v1] Thu, 10 Oct 2019 14:41:10 UTC (85 KB)
[v2] Mon, 2 Dec 2019 15:24:17 UTC (277 KB)
[v3] Fri, 3 Jul 2026 16:10:15 UTC (287 KB)