A generalized Catoni's $\mathrm{M}$-estimator under finite {$\alpha$-th moment assumption} with $\alpha \in (1,2)$

Peng Chen, Xinghu Jin, Xiang Li +1

We generalize the { $\mathrm{M}$-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 f…