Gaussian Mean Testing Made Simple. (arXiv:2210.13706v1 [math.ST])

We study the following fundamental hypothesis testing problem, which we term
Gaussian mean testing. Given i.i.d. samples from a distribution $p$ on
$\mathbb{R}^d$, the task is to distinguish, with high probability, between the
following cases: (i) $p$ is the standard Gaussian distribution,
$\mathcal{N}(0,I_d)$, and (ii) $p$ is a Gaussian $\mathcal{N}(\mu,\Sigma)$ for
some unknown covariance $\Sigma$ and mean $\mu \in \mathbb{R}^d$ satisfying
$\|\mu\|_2 \geq \epsilon$. Recent work gave an algorithm for this testing
problem with the optimal sample complexity of $\Theta(\sqrt{d}/\epsilon^2)$. …

arxiv math mean testing