# On Minimax Detection of Gaussian Stochastic Sequences with Imprecisely Known Means and Covariance Matrices

## TL;DR

This paper investigates the minimax detection of Gaussian sequences with uncertain means and covariances, identifying conditions under which composite hypotheses can be simplified without loss of detection performance.

## Contribution

It characterizes the maximal set of means and covariance matrices allowing composite hypothesis testing to be replaced by simple hypothesis testing without affecting the detection exponent.

## Key findings

- Complete description of the maximal set of parameters
- Conditions for equivalence between composite and simple hypothesis testing
- Analysis of detection exponent under uncertainty

## Abstract

We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with unit variances. For a given false alarm (1st-kind error) probability, the quality of minimax detection is given by the best miss probability (2nd-kind error probability) exponent over a growing observation horizon. We explore the maximal set of means and covariance matrices (composite hypothesis) such that its minimax testing can be replaced with testing a single particular pair consisting of a mean and a covariance matrix (simple hypothesis) without degrading the detection exponent. We completely describe this maximal set.