On the M-Estimator under Third Moment Condition

Rundong Luo, Yiming Chen and Shuai Song
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Rundong Luo: School of Business, Shandong University, Weihai 264209, China
Yiming Chen: Institute for Financial Studies, Shandong University, Jinan 250100, China
Shuai Song: School of Economics, Shandong University, Jinan 250100, China

Mathematics, 2022, vol. 10, issue 10, 1-16

Abstract: Estimating the expected value of a random variable by data-driven methods is one of the most fundamental problems in statistics. In this study, we present an extension of Olivier Catoni’s classical M-estimators of the empirical mean, which focus on the heavy-tailed data by imposing more precise inequalities on exponential moments of Catoni’s estimator. We show that our works behave better than Catoni‘s both in practice and theory. The performances are illustrated in the simulation and real data.

Keywords: M-estimator; Catoni’s estimator; empirical mean (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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