A generalized Neyman-Pearson lemma for sublinear expectations

TL;DR

This paper extends the Neyman-Pearson lemma to sublinear expectations, providing a new method and conditions for optimal tests in this generalized setting, including cases representable by probability measure families.

Contribution

It introduces a novel approach to the Neyman-Pearson lemma under sublinear expectations, weakening previous assumptions and establishing the form of optimal tests.

Findings

Optimal tests retain classical form under sublinear expectations.

Provides sufficient conditions for existence of optimal tests in specific frameworks.

Connects sublinear expectation theory with classical hypothesis testing results.

Abstract

In this paper, the Neyman-Pearson lemma for general sublinear expectations is studied. We weaken the assumptions for sublinear expectations in [1] and give a completely new method to study this problem. Applying Mazur-Orlicz Theorem and the decomposition theorem of finitely additive set functions, we prove that the optimal test still has the reminiscent form as in the classical Neyman-Pearson lemma. Finally, for the special sublinear expectation which can be represented by a family of probability measures, we give a sufficient condition for the existence of the optimal test and show the form of the optimal test selected in L_{c}^1-space which is introduced by Peng [10] in his nonlinear-expectation framework.