Extreme Value Index Estimation for Pareto-Type Tails under Random Censorship and via Generalized Means

The field of statistical extreme value theory (EVT) focuses on estimating parameters associated with extreme events, such as the probability of exceeding a high threshold or determining a high quantile that lies at or beyond the observed data range. Typically, the assumption for univariate data anal...

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Bibliographic Details
Published in:Applied sciences 2024-10, Vol.14 (19), p.8671
Main Authors: Gomes, M. Ivette, Henriques-Rodrigues, Lígia, Neves, M. Manuela, Penalva, Helena
Format: Article
Language:English
Subjects:
Censorship
extreme value theory
generalized means
random censoring
Random variables
statistical computing
statistical semi-parametric inference
survival analysis
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Summary:The field of statistical extreme value theory (EVT) focuses on estimating parameters associated with extreme events, such as the probability of exceeding a high threshold or determining a high quantile that lies at or beyond the observed data range. Typically, the assumption for univariate data analysis is that the sample is complete, independent, identically distributed, or weakly dependent and stationary, drawn from an unknown distribution F. However, in the context of lifetime data, censoring is a common issue. In this work, we consider the case of random censoring for data with a heavy-tailed, Pareto-type distribution. As is common in applications of EVT, the estimation of the extreme value index (EVI) is critical, as it quantifies the tail heaviness of the distribution. The EVI has been extensively studied in the literature. Here, we discuss several classical EVI-estimators and reduced-bias (RB) EVI-estimators within a semi-parametric framework, with a focus on RB EVI-estimators derived from generalized means, which will be applied to both simulated and real survival data.
ISSN:2076-3417
2076-3417
DOI:10.3390/app14198671