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A Partial-Matching Proof of the Neyman--Pearson Lemma
arXiv stat.TH0 views
arXiv:2611.07368v1 Announce Type: new Abstract: Testing seeks to distinguish distributions, whereas matching seeks to identify their common mass. I show that this apparent opposition provides a direct proof of the Neyman--Pearson lemma. Maximal partial matching between the alternative distribution and a scaled null distribution separates them into a common component and two mutually singular residuals. An elementary dual problem then turns this separation into a testing rule: complementary slackness forces rejection on the alternative residual and non-rejection on the scaled-null residual, leaving freedom to randomize at the likelihood-ratio threshold. Thus the optimal test emerges from maximal matching rather than being proposed in advance. The matching profile also determines the optimal power envelope.
Source：https://arxiv.org/abs/2611.07368PreviousNeyman Orthogonalized Specification Tests for Conditional Tail Index ModelsNextSequential Certification of Partially Identified Product Targets: Information Limits and Adaptive Sampling
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