The estimation of the extreme value index (EVI) plays a central role in extreme value theory (EVT), particularly in the statistical modelling of heavy-tailed phenomena. Classical semi-parametric estimators of the EVI are known to suffer from substantial bias, especially for moderate sample sizes and for common choices of the number of upper order statistics. In recent years, several reduced-bias (RB) methodologies have been proposed in order to improve finite-sample performance while preserving asymptotic efficiency. In this paper, we present new classes of nonlinear RB EVI-estimators based on power mean-type and Lehmer mean-type functionals of upper log-excesses. Under a unified higher-order framework, asymptotic representations are derived and bias and variance properties are compared relative to other RB EVI classes introduced in the literature. An asymptotic comparison at optimal levels is conducted to identify regions of the space parameter where the proposed estimators are more efficient. A comprehensive Monte Carlo simulation study assesses the finite sample behaviour of the new estimators for several heavy tailed models. The results show that nonlinear reduced-bias estimators can provide improvements in bias and root mean squared error, although their relative performance depends on the underlying distribution and the choice of the tuning parameter. An application to hydrological data illustrates their practical use and the importance of threshold selection in EVI estimation.

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