Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bounds to the accuracy of inference on heavy tails   The paper suggests a simple method of deriving minimax lower bounds to the
accuracy of statistical inference on heavy tails. A well-known result by Hall
and Welsh (Ann. Statist. 12 (1984) 1079-1084) states that if $\hat{\alpha}_n$
is an estimator of the tail index $\alpha_P$ and $\{z_n\}$ is a sequence of
positive numbers such that
$\sup_{P\in{\mathcal{D}}_r}\mathbb{P}(|\hat{\alpha}_n-\alpha_P|\ge z_n)\to0$,
where ${\mathcal{D}}_r$ is a certain class of heavy-tailed distributions, then
$z_n\gg n^{-r}$. The paper presents a non-asymptotic lower bound to the
probabilities $\mathbb{P}(|\hat{\alpha}_n-\alpha_P|\ge z_n)$. We also establish
non-uniform lower bounds to the accuracy of tail constant and extreme quantiles
estimation. The results reveal that normalising sequences of robust estimators
should depend in a specific way on the tail index and the tail constant.

6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph