Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Sub-Gaussian Mean Estimation in $\mathbb{R}$   We revisit the problem of estimating the mean of a real-valued distribution,
presenting a novel estimator with sub-Gaussian convergence: intuitively, "our
estimator, on any distribution, is as accurate as the sample mean is for the
Gaussian distribution of matching variance." Crucially, in contrast to prior
works, our estimator does not require prior knowledge of the variance, and
works across the entire gamut of distributions with bounded variance, including
those without any higher moments. Parameterized by the sample size $n$, the
failure probability $\delta$, and the variance $\sigma^2$, our estimator is
accurate to within $\sigma\cdot(1+o(1))\sqrt{\frac{2\log\frac{1}{\delta}}{n}}$,
tight up to the $1+o(1)$ factor. Our estimator construction and analysis gives
a framework generalizable to other problems, tightly analyzing a sum of
dependent random variables by viewing the sum implicitly as a 2-parameter
$\psi$-estimator, and constructing bounds using mathematical programming and
duality techniques.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th