New Upper Bounds in the Hypothesis Testing Problem with Information Constraints

TL;DR

This paper investigates the minimal amount of auxiliary information needed to perform optimal hypothesis testing when some data are unobserved, deriving bounds and estimates for this information.

Contribution

It introduces new bounds on the minimal auxiliary information required for hypothesis testing with incomplete data, advancing understanding of information constraints in statistical inference.

Findings

Derived estimates for minimal auxiliary information

Established bounds matching optimal inference performance

Provided theoretical insights into information sufficiency

Abstract

We consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make the best statistical inference? In particular, what is the minimum information sufficient to obtain the same results as if we directly observed all the data? We derive estimates for this minimum information and some other similar results.