The Neyman-Pearson lemma for convex expectations
Probability
2019-12-11 v2
Abstract
We study the Neyman-Pearson problem for convex expectations on L^{\infty}(\mu). The existence of the optimal test is given. Without assuming that the level sets of penalty functions are weakly compact, we prove that the optimal tests for convex expectations on L^{\infty}(\mu) are just the classical Neyman-Pearson tests between a fixed representative pair of simple hypotheses. Then we show that the Neyman-Pearson problem for convex expectations on L^{1}(\mu) can be solved similarly.
Cite
@article{arxiv.1909.01518,
title = {The Neyman-Pearson lemma for convex expectations},
author = {Chuanfeng Sun and Shaolin Ji},
journal= {arXiv preprint arXiv:1909.01518},
year = {2019}
}