Extreme Value Theory plays an important role to provide approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the \textcolor{red}{generalised Pareto distribution} $H_\gamma(x)$ as an approximation of the distribution $F_t(s(t)x)$ of the excesses over a threshold $t$, where $s(t)$ is a suitable norming function. In this paper we study the rate of convergence of $F_t(s(t)\cdot)$ to $H_\gamma$ in variational and Hellinger distances and translate it into that regarding the Kullback-Leibler divergence between the respective densities.

Strong convergence of peaks over a threshold

Padoan, Simone A.
Methodology
;
Rizzelli, Stefano
2023

Abstract

Extreme Value Theory plays an important role to provide approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the \textcolor{red}{generalised Pareto distribution} $H_\gamma(x)$ as an approximation of the distribution $F_t(s(t)x)$ of the excesses over a threshold $t$, where $s(t)$ is a suitable norming function. In this paper we study the rate of convergence of $F_t(s(t)\cdot)$ to $H_\gamma$ in variational and Hellinger distances and translate it into that regarding the Kullback-Leibler divergence between the respective densities.
File in questo prodotto:
File Dimensione Formato  
acceptance_letter_padoan.pdf

non disponibili

Descrizione: Lettera di accettazione
Tipologia: Allegato per valutazione Bocconi (Attachment for Bocconi evaluation)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 132.45 kB
Formato Adobe PDF
132.45 kB Adobe PDF   Visualizza/Apri
Strong_POT_final.pdf

non disponibili

Descrizione: versione finale accettata
Tipologia: Documento in Pre-print (Pre-print document)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 354.75 kB
Formato Adobe PDF
354.75 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/4057176
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact