# On asymptotically minimax nonparametric detection of signal in Gaussian white noise

## TL;DR

This paper develops asymptotically minimax tests for detecting signals in Gaussian white noise within Besov space constraints, focusing on challenging alternative sets with small $L_2$ balls removed.

## Contribution

It introduces strong asymptotically minimax tests for nonparametric signal detection in Gaussian noise, considering complex Besov space alternatives.

## Key findings

- Identification of strong asymptotically minimax tests
- Analysis of alternative sets with small $L_2$ balls removed
- Theoretical characterization of detection boundaries

## Abstract

For the problem of nonparametric detection of signal in Gaussian white noise we point out strong asymptotically minimax tests. The sets of alternatives are a ball in Besov space $B^r_{2\infty}$ with "small" balls in $L_2$ removed.