A simple estimator for the $\mathcal{M}$-index of functions in $\mathcal{M}$

Abstract: An estimator for the $\M$-index of functions of $\mathcal{M}$, a larger class than the class of regularly varying (RV) functions, is proposed. This index is the tail index of RV functions and this estimator is thus a new one on the class of RV functions. This estimator satisfies, assuming suitable conditions, strong consistency. Asymptotic normality of this estimator is proved for a large class of RV functions, showing a better performance than some well-known estimators. Illustrations with simulated and real life datasets are provided.