Asymptotic estimation of right and left kurtosis measures, with applications to finance

Inequality-based measures of right and left kurtosis have recently emerged as an effective alternative to the conventional fourth moment coefficient of kurtosis. In this contribution we show that the theory of L-statistics provides a convenient framework for the construction of empirical estimators for the new measures and the investigation of their asymptotic properties. Natural applications arise in financial contexts, in which the proposed estimators provide both a more robust and a more informative picture of the kurtosis risk embedded in market returns.