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2021 A generalized Catoni’s M-estimator under finite α-th moment assumption with α(1,2)
Peng Chen, Xinghu Jin, Xiang Li, Lihu Xu
Author Affiliations +
Electron. J. Statist. 15(2): 5523-5544 (2021). DOI: 10.1214/21-EJS1911

Abstract

We generalize Catoni’s M-estimator, put forward in [3] by Catoni under finite variance assumption, to the case in which distributions can have finite α-th moment with α(1,2). Our approach, inspired by the Taylor-like expansion developed in [4], is via slightly modifying the influence function φ in [3]. A deviation bound is established for this generalized estimator, and coincides with that in [3] as α2. Experiment shows that our M-estimator performs better than the empirical mean, the smaller the α is, the better the performance will be. As an application, we study an 1 regression considered by Zhang et al. [19], who assumed that samples have finite variance, under finite α-th moment assumption with α(1,2).

Acknowledgments

LX is supported in part by NSFC grant (No. 12071499), Macao S.A.R grant FDCT 0090/2019/A2 and University of Macau grant MYRG2018-00133-FST. We are grateful to the referee whose numerous comments and suggestions have helped to greatly improve the presentation of this paper.

Citation

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Peng Chen. Xinghu Jin. Xiang Li. Lihu Xu. "A generalized Catoni’s M-estimator under finite α-th moment assumption with α(1,2)." Electron. J. Statist. 15 (2) 5523 - 5544, 2021. https://doi.org/10.1214/21-EJS1911

Information

Received: 1 October 2020; Published: 2021
First available in Project Euclid: 15 December 2021

arXiv: 2010.05008
Digital Object Identifier: 10.1214/21-EJS1911

Subjects:
Primary: 62G05
Secondary: 62G35

Keywords: Catoni’s M-estimator , deviation bound , empirical mean , ℓ1 regression , α-th moment

Vol.15 • No. 2 • 2021
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