TY - JOUR

T1 - Fundamentals of non-parametric statistical inference for integrated quantiles

AU - Грибкова, Надежда Викторовна

AU - Wang, Mengqi

AU - Zitikis, Ričardas

N1 - Nadezhda V. Gribkova, Mengqi Wang, Ričardas Zitikis, Fundamentals of non-parametric statistical inference for integrated quantiles, Risk Sciences, Volume 2, 2026, 100026, ISSN 2950-6298, https://doi.org/10.1016/j.risk.2025.100026

PY - 2026/1/27

Y1 - 2026/1/27

N2 - We present a general non-parametric statistical inference theory for integrals of quantiles without assuming any specific sampling design or dependence structure. Technical considerations are accompanied by examples and discussions, including those pertaining to the bias of empirical estimators. To illustrate how the general results can be adapted to specific situations, we derive – at a stroke and under minimal conditions – consistency and asymptotic normality of the empirical tail-value-at-risk, Lorenz and Gini curves at any probability level in the case of the simple random sampling, thus facilitating a comparison of our results with what is already known in the literature. Results, notes and references concerning dependent (i.e., time series) data are also offered. As a by-product, our general results provide new and unified proofs of large-sample properties of a number of classical statistical estimators, such as trimmed means, and give additional insights into the origins of, and the reasons for, various necessary and sufficient conditions.

AB - We present a general non-parametric statistical inference theory for integrals of quantiles without assuming any specific sampling design or dependence structure. Technical considerations are accompanied by examples and discussions, including those pertaining to the bias of empirical estimators. To illustrate how the general results can be adapted to specific situations, we derive – at a stroke and under minimal conditions – consistency and asymptotic normality of the empirical tail-value-at-risk, Lorenz and Gini curves at any probability level in the case of the simple random sampling, thus facilitating a comparison of our results with what is already known in the literature. Results, notes and references concerning dependent (i.e., time series) data are also offered. As a by-product, our general results provide new and unified proofs of large-sample properties of a number of classical statistical estimators, such as trimmed means, and give additional insights into the origins of, and the reasons for, various necessary and sufficient conditions.

KW - Integrated quantiles

KW - Expected shortfall

KW - Tail value at risk

KW - Lorenz curve

KW - Gini curve

KW - Trimmed mean

KW - L-statistic

KW - Distortion risk measure

KW - Time series

KW - S-mixing

KW - M-mixing

UR - https://www.mendeley.com/catalogue/4ad94730-e9d5-3bd5-8403-c3e77c35599c/

U2 - 10.1016/j.risk.2025.100026

DO - 10.1016/j.risk.2025.100026

M3 - Article

VL - 2

JO - Risk Sciences

JF - Risk Sciences

SN - 2950-6298

IS - 1

M1 - 100026

ER -