A distribution-free valid p-value for finite samples of bounded random variables

Joaquin Alvarez

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arXiv · 2405.08975

A distribution-free valid p-value for finite samples of bounded random variables

Joaquin Alvarez

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Abstract

We build a valid p-value based on a concentration inequality for bounded random variables introduced by Pelekis, Ramon and Wang. The motivation behind this work is the calibration of predictive algorithms in a distribution-free setting. The super-uniform p-value is tighter than Hoeffding and Bentkus alternatives in certain regions. Even though we are motivated by a calibration setting in a machine learning context, the ideas presented in this work are also relevant in classical statistical inference. Furthermore, we compare the power of a collection of valid p- values for bounded losses, which are presented in previous literature.

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stat.ML cs.LG math.ST stat.TH

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BibTeX RIS

Joaquin Alvarez. 2024-05-14. A distribution-free valid p-value for finite samples of bounded random variables. https://arxiv.org/abs/2405.08975

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