On the M-Estimator under Third Moment Condition

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