= Olivier Catoni
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<Olivier Catoni> develops methods for <robust statistics>. His work on the <mean> and <variance> constructs <M-estimators> with deviation guarantees for <heavy-tailed distributions> under moment assumptions.<Challenging the empirical mean and empirical variance: a deviation study by Olivier Catoni>[Abstract and Section2]{ref}
The <sample mean> lets a single very large observation exert arbitrarily large influence. Catoni's construction replaces a linear estimating equation by a controlled nonlinear function of each residual. With an appropriate tuning parameter, a mean estimator can achieve Gaussian-order deviation bounds at a chosen confidence level under bounded <variance>, even when the observations are not <normally distributed>. The tuning and assumptions are part of the guarantee; the result does not assert that one fixed setting automatically works at every confidence level.<Challenging the empirical mean and empirical variance: a deviation study by Olivier Catoni>[Equations2.1–2.3 and Proposition2.4]{ref}
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