  In the setting of entangled single-sample distributions, the goal is to
estimate some common parameter shared by a family of $n$ distributions, given
one single sample from each distribution. This paper studies mean estimation
for entangled single-sample Gaussians that have a common mean but different
unknown variances. We propose the subset-of-signals model where an unknown
subset of $m$ variances are bounded by 1 while there are no assumptions on the
other variances. In this model, we analyze a simple and natural method based on
iteratively averaging the truncated samples, and show that the method achieves
error $O \left(\frac{\sqrt{n\ln n}}{m}\right)$ with high probability when
$m=\Omega(\sqrt{n\ln n})$, matching existing bounds for this range of $m$. We
further prove lower bounds, showing that the error is
$\Omega\left(\left(\frac{n}{m^4}\right)^{1/2}\right)$ when $m$ is between
$\Omega(\ln n)$ and $O(n^{1/4})$, and the error is
$\Omega\left(\left(\frac{n}{m^4}\right)^{1/6}\right)$ when $m$ is between
$\Omega(n^{1/4})$ and $O(n^{1 - \epsilon})$ for an arbitrarily small
$\epsilon>0$, improving existing lower bounds and extending to a wider range of
$m$.
