Standard

Weighted allocations, their concomitant-based estimators, and asymptotics. / Gribkova, Nadezhda ; Zitikis, Ričardas.

In: Annals of the Institute of Statistical Mathematics, Vol. 71, No. 4, 08.2019, p. 811–835.

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

Harvard

Gribkova, N & Zitikis, R 2019, 'Weighted allocations, their concomitant-based estimators, and asymptotics', Annals of the Institute of Statistical Mathematics, vol. 71, no. 4, pp. 811–835. https://doi.org/10.1007/s10463-018-0660-2

APA

Gribkova, N., & Zitikis, R. (2019). Weighted allocations, their concomitant-based estimators, and asymptotics. Annals of the Institute of Statistical Mathematics, 71(4), 811–835. https://doi.org/10.1007/s10463-018-0660-2

Vancouver

Gribkova N, Zitikis R. Weighted allocations, their concomitant-based estimators, and asymptotics. Annals of the Institute of Statistical Mathematics. 2019 Aug;71(4):811–835. https://doi.org/10.1007/s10463-018-0660-2

Author

Gribkova, Nadezhda ; Zitikis, Ričardas. / Weighted allocations, their concomitant-based estimators, and asymptotics. In: Annals of the Institute of Statistical Mathematics. 2019 ; Vol. 71, No. 4. pp. 811–835.

BibTeX

@article{c47ea155bf414f79b7c98652c5364e85,
title = "Weighted allocations, their concomitant-based estimators, and asymptotics",
abstract = "Various members of the class of weighted insurance premiums and risk capital allocation rules have been researched from a number of perspectives. Corresponding formulas in the case of parametric families of distributions have been derived, and they have played a pivotal role when establishing parametric statistical inference in the area. Nonparametric inference results have also been derived in special cases such as the tail conditional expectation, distortion risk measure, and several members of the class of weighted premiums. For weighted allocation rules, however, nonparametric inference results have not yet been adequately developed. In the present paper, therefore, we put forward empirical estimators for the weighted allocation rules and establish their consistency and asymptotic normality under practically sound conditions. Intricate statistical considerations rely on the theory of induced order statistics, known as concomitants.",
keywords = "Weighted allocation, Insurance premium, Concomitant, Consistency, Asymptotic normality, Weighted allocation, Insurance premium, Concomitant, Consistency, Asymptotic normality",
author = "Nadezhda Gribkova and Ri{\v c}ardas Zitikis",
note = "Gribkova, N., & Zitikis, R. (2019). Weighted allocations, their concomitant-based estimators, and asymptotics. Annals of the Institute of Statistical Mathematics, 71(4), 811–835. https://doi.org/10.1007/s10463-018-0660-2",
year = "2019",
month = aug,
doi = "10.1007/s10463-018-0660-2",
language = "English",
volume = "71",
pages = "811–835",
journal = "Annals of the Institute of Statistical Mathematics",
issn = "0020-3157",
publisher = "Springer Nature",
number = "4",

}

RIS

TY - JOUR

T1 - Weighted allocations, their concomitant-based estimators, and asymptotics

AU - Gribkova, Nadezhda

AU - Zitikis, Ričardas

N1 - Gribkova, N., & Zitikis, R. (2019). Weighted allocations, their concomitant-based estimators, and asymptotics. Annals of the Institute of Statistical Mathematics, 71(4), 811–835. https://doi.org/10.1007/s10463-018-0660-2

PY - 2019/8

Y1 - 2019/8

N2 - Various members of the class of weighted insurance premiums and risk capital allocation rules have been researched from a number of perspectives. Corresponding formulas in the case of parametric families of distributions have been derived, and they have played a pivotal role when establishing parametric statistical inference in the area. Nonparametric inference results have also been derived in special cases such as the tail conditional expectation, distortion risk measure, and several members of the class of weighted premiums. For weighted allocation rules, however, nonparametric inference results have not yet been adequately developed. In the present paper, therefore, we put forward empirical estimators for the weighted allocation rules and establish their consistency and asymptotic normality under practically sound conditions. Intricate statistical considerations rely on the theory of induced order statistics, known as concomitants.

AB - Various members of the class of weighted insurance premiums and risk capital allocation rules have been researched from a number of perspectives. Corresponding formulas in the case of parametric families of distributions have been derived, and they have played a pivotal role when establishing parametric statistical inference in the area. Nonparametric inference results have also been derived in special cases such as the tail conditional expectation, distortion risk measure, and several members of the class of weighted premiums. For weighted allocation rules, however, nonparametric inference results have not yet been adequately developed. In the present paper, therefore, we put forward empirical estimators for the weighted allocation rules and establish their consistency and asymptotic normality under practically sound conditions. Intricate statistical considerations rely on the theory of induced order statistics, known as concomitants.

KW - Weighted allocation

KW - Insurance premium

KW - Concomitant

KW - Consistency

KW - Asymptotic normality

KW - Weighted allocation

KW - Insurance premium

KW - Concomitant

KW - Consistency

KW - Asymptotic normality

UR - http://www.scopus.com/inward/record.url?scp=85045070588&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/weighted-allocations-concomitantbased-estimators-asymptotics

U2 - 10.1007/s10463-018-0660-2

DO - 10.1007/s10463-018-0660-2

M3 - Article

VL - 71

SP - 811

EP - 835

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 4

ER -

ID: 34784957