Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalized Catoni's ${\rm M}$-estimator under finite {$\alpha$-th
  moment assumption} with $\alpha \in (1,2)$   We generalize the { ${\rm M}$-estimator} put forward by Catoni in his seminal
paper [C12] to the case in which samples can have finite $\alpha$-th moment
with $\alpha \in (1,2)$ rather than finite variance, our approach is by
slightly modifying the influence function $\varphi$ therein. The choice of the
new influence function is inspired by the Taylor-like expansion developed in
[C-N-X]. We obtain a deviation bound of the estimator, as $\alpha \rightarrow
2$, this bound is the same as that in [C12]. Experiment shows that our
generalized ${\rm M}$-estimator performs better than the empirical mean
estimator, the smaller the $\alpha$ is, the better the performance will be. As
an application, we study an $\ell_{1}$ regression considered by Zhang et al.
[Z-Z] who assumed that samples have finite variance, and relax their assumption
to be finite {$\alpha$-th} moment with $\alpha \in (1,2)$.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th