Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adaptive and minimax optimal estimation of the tail coefficient   We consider the problem of estimating the tail index $\alpha$ of a
distribution satisfying a $(\alpha, \beta)$ second-order Pareto-type condition,
where \beta is the second-order coefficient. When $\beta$ is available, it was
previously proved that $\alpha$ can be estimated with the oracle rate
$n^{-\beta/(2\beta+1)}$. On the contrary, when $\beta$ is not available,
estimating $\alpha$ with the oracle rate is challenging; so additional
assumptions that imply the estimability of $\beta$ are usually made. In this
paper, we propose an adaptive estimator of $\alpha$, and show that this
estimator attains the rate $(n/\log\log n)^{-\beta/(2\beta+1)}$ without a
priori knowledge of $\beta$ and any additional assumptions. Moreover, we prove
that this $(\log\log n)^{\beta/(2\beta+1)}$ factor is unavoidable by obtaining
the companion lower bound.

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org