Open Access
2023 Estimation of tail parameters with missing largest observations
Jan Beirlant, Martin Bladt, Gao Maribe, Andrehette Verster
Author Affiliations +
Electron. J. Statist. 17(2): 3728-3761 (2023). DOI: 10.1214/23-EJS2191


The setting where an unknown number m of the largest data is missing from an underlying Pareto-type distribution is considered. Solutions are provided for estimating the extreme value index, the number of missing data and extreme quantiles. Asymptotic results of the parameter estimators and an adaptive selection method for the number of top data used in the estimation are proposed for the case where all missing data are beyond the observed data. An estimator of the number of missing extremes spread over the largest observed data is also proposed. To this purpose, a key component is a likelihood solution based on exponential representations of spacings between the largest observations. An effective and fast optimization procedure is established using regularization, and simulation experiments are provided. The methodology is illustrated with a dataset from the diamond mining industry, where large-carat diamonds are expected to be missing.


Download Citation

Jan Beirlant. Martin Bladt. Gao Maribe. Andrehette Verster. "Estimation of tail parameters with missing largest observations." Electron. J. Statist. 17 (2) 3728 - 3761, 2023.


Received: 1 April 2023; Published: 2023
First available in Project Euclid: 7 December 2023

Digital Object Identifier: 10.1214/23-EJS2191

Keywords: extreme value index , high quantiles , missing observations , regularization

Vol.17 • No. 2 • 2023
Back to Top