Estimation of tail parameters with missing largest observations
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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
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TY - JOUR
T1 - Estimation of tail parameters with missing largest observations
AU - Beirlant, Jan
AU - Bladt, Martin
AU - Maribe, Gao
AU - Verster, Andrehette
N1 - Publisher Copyright: © 2023, Institute of Mathematical Statistics. All rights reserved.
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