Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator

Yizhou Li; Paweł Polak

doi:10.1016/j.spl.2025.110411

Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator

Yizhou Li
, Paweł Polak

Applied Mathematics and Statistics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

Abstract

We show weak convergence of the empirical Conditional Value-at-Risk (CVaR) in functional space and the asymptotic normality of the CVaR-based Pickands estimator from Chen (2021). These results demonstrate that the CVaR-based estimator has significantly lower asymptotic variance than analogous VaR-based constructions.

Original language	English
Article number	110411
Journal	Statistics and Probability Letters
Volume	223
DOIs	https://doi.org/10.1016/j.spl.2025.110411
State	Published - Aug 2025

Keywords

Asymptotic normality
Conditional Value-at-Risk
Extreme value index
Pickands estimator
Second-order regular variation

Access to Document

10.1016/j.spl.2025.110411

Cite this

@article{1706e4f5e9e3415fa86d2d787da03f80,

title = "Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator",

abstract = "We show weak convergence of the empirical Conditional Value-at-Risk (CVaR) in functional space and the asymptotic normality of the CVaR-based Pickands estimator from Chen (2021). These results demonstrate that the CVaR-based estimator has significantly lower asymptotic variance than analogous VaR-based constructions.",

keywords = "Asymptotic normality, Conditional Value-at-Risk, Extreme value index, Pickands estimator, Second-order regular variation",

author = "Yizhou Li and Pawe{\l} Polak",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier B.V.",

year = "2025",

month = aug,

doi = "10.1016/j.spl.2025.110411",

language = "English",

volume = "223",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

}

TY - JOUR

T1 - Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator

AU - Li, Yizhou

AU - Polak, Paweł

PY - 2025/8

Y1 - 2025/8

N2 - We show weak convergence of the empirical Conditional Value-at-Risk (CVaR) in functional space and the asymptotic normality of the CVaR-based Pickands estimator from Chen (2021). These results demonstrate that the CVaR-based estimator has significantly lower asymptotic variance than analogous VaR-based constructions.

AB - We show weak convergence of the empirical Conditional Value-at-Risk (CVaR) in functional space and the asymptotic normality of the CVaR-based Pickands estimator from Chen (2021). These results demonstrate that the CVaR-based estimator has significantly lower asymptotic variance than analogous VaR-based constructions.

KW - Asymptotic normality

KW - Conditional Value-at-Risk

KW - Extreme value index

KW - Pickands estimator

KW - Second-order regular variation

UR - https://www.scopus.com/pages/publications/105000984820

U2 - 10.1016/j.spl.2025.110411

DO - 10.1016/j.spl.2025.110411

M3 - Article

AN - SCOPUS:105000984820

SN - 0167-7152

VL - 223

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 110411

ER -

Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this