On Hypothesis Testing via a Tunable Loss

TL;DR

This paper explores hypothesis testing using a tunable loss function, deriving classical results like Neyman--Pearson and Chernoff bounds, and establishing the optimal error exponents in this new framework.

Contribution

It introduces a novel hypothesis testing approach with a tunable loss, extending classical statistical results to this new setting.

Findings

Optimal error exponent matches classical Neyman--Pearson results

Provides lower bounds for Bayesian error exponents

Extends classical hypothesis testing theory to tunable loss functions

Abstract

We consider a problem of simple hypothesis testing using a randomized test via a tunable loss function proposed by Liao \textit{et al}. In this problem, we derive results that correspond to the Neyman--Pearson lemma, the Chernoff--Stein lemma, and the Chernoff-information in the classical hypothesis testing problem. Specifically, we prove that the optimal error exponent of our problem in the Neyman--Pearson's setting is consistent with the classical result. Moreover, we provide lower bounds of the optimal Bayesian error exponent.