Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Confidence regions and minimax rates in outlier-robust estimation on the
  probability simplex   We consider the problem of estimating the mean of a distribution supported by
the $k$-dimensional probability simplex in the setting where an $\varepsilon$
fraction of observations are subject to adversarial corruption. A simple
particular example is the problem of estimating the distribution of a discrete
random variable. Assuming that the discrete variable takes $k$ values, the
unknown parameter $\boldsymbol \theta$ is a $k$-dimensional vector belonging to
the probability simplex. We first describe various settings of contamination
and discuss the relation between these settings. We then establish minimax
rates when the quality of estimation is measured by the total-variation
distance, the Hellinger distance, or the $\mathbb L^2$-distance between two
probability measures. We also provide confidence regions for the unknown mean
that shrink at the minimax rate. Our analysis reveals that the minimax rates
associated to these three distances are all different, but they are all
attained by the sample average. Furthermore, we show that the latter is
adaptive to the possible sparsity of the unknown vector. Some numerical
experiments illustrating our theoretical findings are reported.

19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat