On the Equivalence of $f$-Divergence Balls and Density Bands in Robust Detection
Michael Fauß, Abdelhak M. Zoubir, H. Vincent Poor
Abstract
The paper deals with minimax optimal statistical tests for two composite hypotheses, where each hypothesis is defined by a nonparametric uncertainty set of feasible distributions. It is shown that for every pair of uncertainty sets of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f$</tex> -divergence-ball type, a pair of uncertainty sets of the density-band type can be constructed, which is equivalent in the sense that it admits the same pair of least favorable distributions. This result implies that robust tests under <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f$</tex> -divergence-ball uncertainty, which are typically only minimax optimal for the single sample case, are also fixed sample size minimax optimal with respect to the equivalent density-band uncertainty sets.
BibTeX
@inproceedings{icassp2018_ontheequivalence,
title = {On the Equivalence of $f$-Divergence Balls and Density Bands in Robust Detection},
author = {Michael Fauß and Abdelhak M. Zoubir and H. Vincent Poor},
booktitle = {ICASSP 2018},
year = {2018}
}