Weighted Parameter Estimators of the Generalized Extreme Value Distribution in the Presence of Missing Observations

TL;DR

This paper introduces weighted estimators for the generalized extreme value distribution to address bias caused by missing data in extreme value analysis, validated through simulations and real tidal gauge data.

Contribution

It proposes novel weighted maximum likelihood and moment-based estimators specifically designed for GEV parameters with missing observations.

Findings

Weighted estimators reduce bias in GEV parameter estimation.

Simulation results demonstrate improved accuracy over traditional methods.

Application to tidal gauge data confirms practical effectiveness.

Abstract

Missing data occur in a variety of applications of extreme value analysis. In the block maxima approach to an extreme value analysis, missingness is often handled by either ignoring missing observations or dropping a block of observations from the analysis. However, in some cases, missingness may occur due to equipment failure during an extreme event, which can lead to bias in estimation. In this work, we propose weighted maximum likelihood and weighted moment-based estimators for the generalized extreme value distribution parameters to account for the presence of missing observations. We validate the procedures through an extensive simulation study and apply the estimation methods to data from multiple tidal gauges on the Eastern coast of Canada.