Tilting maximum Lq-Likelihood estimation for extreme values drawing on block maxima

TL;DR

This paper proposes a novel tilting maximum Lq-likelihood method for better estimation of extreme values from small samples, enhancing risk assessment in fields like natural disasters and public health.

Contribution

It introduces a new Lq-likelihood variant linked with a deformed logarithm, improving extreme value estimation in small sample block maxima scenarios.

Findings

Enhanced accuracy in extreme value estimation demonstrated through simulations

Significant improvements in return-level estimation for risk assessment

Application to public health data illustrates practical benefits

Abstract

One of the most common anticipated difficulties in applying mainstream maximum likelihood inference upon extreme values is articulated on the scarcity of extreme observations for bringing the extreme value theorem to hold across a series of maxima. This paper introduces a new variant of the Lq-likelihood method through its linkage with a particular deformed logarithm which preserves the self-dual property of the standard logarithm. Since the focus is on relatively small samples consisting of those maximum values within each sub-sampled block (by splitting the sample into blocks of equal length), the maximum Lq estimation will favour reducing uncertainty associated with the variance leaving the bias unchallenged. A comprehensive simulation study demonstrates that the introduction of a more sophisticated treatment of maximum likelihood improves the estimation of extreme characteristics, with significant implications for return-level estimation which is a crucial component in risk assessment for many operational settings prone to extreme hazards, such as earthquakes, floods or epidemics. We provide an illustrative example of how the proposed tilting of Lq-likelihood can improve inference on extreme events by drawing on public health data.