Old Bands, New Tracks---Revisiting the Band Model for Robust Hypothesis Testing

TL;DR

This paper revisits the density band model for robust hypothesis testing, introducing a unified criterion for least favorable distributions, a simplified implicit definition, and a fixed-point algorithm for practical computation.

Contribution

It proposes a novel unified criterion for least favorable distributions, simplifying their computation under band uncertainties.

Findings

A new implicit definition of least favorable distributions requiring only two scalar values.

A fixed-point algorithm for iterative calculation of least favorable distributions.

Discussion of three robust tests derived from band models with numerical illustration.

Abstract

The density band model proposed by Kassam for robust hypothesis testing is revisited in this paper. First, a novel criterion for the general characterization of least favorable distributions is proposed, which unifies existing results. This criterion is then used to derive an implicit definition of the least favorable distributions under band uncertainties. In contrast to the existing solution, it only requires two scalar values to be determined and eliminates the need for case-by-case statements. Based on this definition, a generic fixed-point algorithm is proposed that iteratively calculates the least favorable distributions for arbitrary band specifications. Finally, three different types of robust tests that emerge from band models are discussed and a numerical example is presented to illustrate their potential use in practice.