Extreme Value Index Estimation for Pareto-Type Tails under Random Censorship and via Generalized Means
Source abstract
Abstract
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.
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Research context
OpenAlex topics: Financial Risk and Volatility Modeling · Stochastic processes and financial applications · Probability and Risk Models
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Centro de Estatística e Aplicações, Universidade de Lisboa (CEAUL), Campo Grande, 1749-016 Lisboa, Portugal
Departamento de Estatística e Investigação Operacional, Faculdade de Ciências, Universidade de Lisboa (UL), 1749-016 Lisboa, Portugal
Departamento de Matemática, Escola de Ciências e Tecnologia, and Centro de Investigação em Matemática e Aplicações (CIMA), Universidade de Évora, 7000-671 Évora, Portugal
Instituto Superior de Agronomia (ISA), Universidade de Lisboa (UL), 1349-017 Lisboa, Portugal
Departamento de Economia e Gestão, Escola Superior de Ciências Empresariais, Instituto Politécnico de Setúbal, 2910-761 Setúbal, Portugal
Funding
FCT—Fundação para a Ciência e a Tecnologia · HiTEc Cost Action
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