Estimation of tail parameters with missing largest observations

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Standard

Estimation of tail parameters with missing largest observations. / Beirlant, Jan; Bladt, Martin; Maribe, Gao; Verster, Andrehette.

I: Electronic Journal of Statistics, Bind 17, Nr. 2, 2023, s. 3728-3761.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Beirlant, J, Bladt, M, Maribe, G & Verster, A 2023, 'Estimation of tail parameters with missing largest observations', Electronic Journal of Statistics, bind 17, nr. 2, s. 3728-3761. https://doi.org/10.1214/23-EJS2191

APA

Beirlant, J., Bladt, M., Maribe, G., & Verster, A. (2023). Estimation of tail parameters with missing largest observations. Electronic Journal of Statistics, 17(2), 3728-3761. https://doi.org/10.1214/23-EJS2191

Vancouver

Beirlant J, Bladt M, Maribe G, Verster A. Estimation of tail parameters with missing largest observations. Electronic Journal of Statistics. 2023;17(2):3728-3761. https://doi.org/10.1214/23-EJS2191

Author

Beirlant, Jan ; Bladt, Martin ; Maribe, Gao ; Verster, Andrehette. / Estimation of tail parameters with missing largest observations. I: Electronic Journal of Statistics. 2023 ; Bind 17, Nr. 2. s. 3728-3761.

Bibtex

@article{644841990d8a4621a4c85bf4422b609d,

title = "Estimation of tail parameters with missing largest observations",

abstract = "The setting where an unknown number m of the largest data is missing from an underlying Pareto-type distribution is considered. So-lutions are provided for estimating the extreme value index, the number of missing data and extreme quantiles. Asymptotic results of the parameter estimators and an adaptive selection method for the number of top data used in the estimation are proposed for the case where all missing data are beyond the observed data. An estimator of the number of missing extremes spread over the largest observed data is also proposed. To this purpose, a key component is a likelihood solution based on exponential representations of spacings between the largest observations. An effective and fast optimization procedure is established using regularization, and simulation experiments are provided. The methodology is illustrated with a dataset from the diamond mining industry, where large-carat diamonds are expected to be missing.",

keywords = "Extreme value index, high quantiles, missing observations, regularization",

author = "Jan Beirlant and Martin Bladt and Gao Maribe and Andrehette Verster",

year = "2023",

doi = "10.1214/23-EJS2191",

language = "English",

volume = "17",

pages = "3728--3761",

journal = "Electronic Journal of Statistics",

issn = "1935-7524",

publisher = "nstitute of Mathematical Statistics",

number = "2",

}

RIS

TY - JOUR

T1 - Estimation of tail parameters with missing largest observations

AU - Beirlant, Jan

AU - Bladt, Martin

AU - Maribe, Gao

AU - Verster, Andrehette

PY - 2023

Y1 - 2023

N2 - The setting where an unknown number m of the largest data is missing from an underlying Pareto-type distribution is considered. So-lutions are provided for estimating the extreme value index, the number of missing data and extreme quantiles. Asymptotic results of the parameter estimators and an adaptive selection method for the number of top data used in the estimation are proposed for the case where all missing data are beyond the observed data. An estimator of the number of missing extremes spread over the largest observed data is also proposed. To this purpose, a key component is a likelihood solution based on exponential representations of spacings between the largest observations. An effective and fast optimization procedure is established using regularization, and simulation experiments are provided. The methodology is illustrated with a dataset from the diamond mining industry, where large-carat diamonds are expected to be missing.

AB - The setting where an unknown number m of the largest data is missing from an underlying Pareto-type distribution is considered. So-lutions are provided for estimating the extreme value index, the number of missing data and extreme quantiles. Asymptotic results of the parameter estimators and an adaptive selection method for the number of top data used in the estimation are proposed for the case where all missing data are beyond the observed data. An estimator of the number of missing extremes spread over the largest observed data is also proposed. To this purpose, a key component is a likelihood solution based on exponential representations of spacings between the largest observations. An effective and fast optimization procedure is established using regularization, and simulation experiments are provided. The methodology is illustrated with a dataset from the diamond mining industry, where large-carat diamonds are expected to be missing.

KW - Extreme value index

KW - high quantiles

KW - missing observations

KW - regularization

U2 - 10.1214/23-EJS2191

DO - 10.1214/23-EJS2191

M3 - Journal article

AN - SCOPUS:85182467915

VL - 17

SP - 3728

EP - 3761

JO - Electronic Journal of Statistics

JF - Electronic Journal of Statistics

SN - 1935-7524

IS - 2

ER -

ID: 380304082

Institut for Matematiske Fag