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  • Assessment of heavy tailed data and its compound sums has many applications in insurance, auditing and operational risk capital assessment among others. In this paper, we compare the classical estimators (maximum likelihood, QQ and moment estimators) with the recently introduced robust estimators of “generalized median, “trimmed mean and estimators based on t-score moments. We derive the exact distribution of the likelihood ratio tests of homogeneity and simple hypothesis on the tail index of a two-parameter Pareto model. Such exact tests support the assessment of the performance of estimators. In particular, we discuss some problems that one can encounter when misemploying the log-normal assumption based methods supported by the Basel II framework. Real data and simulated examples illustrate the methods.
  • Assessment of heavy tailed data and its compound sums has many applications in insurance, auditing and operational risk capital assessment among others. In this paper, we compare the classical estimators (maximum likelihood, QQ and moment estimators) with the recently introduced robust estimators of “generalized median, “trimmed mean and estimators based on t-score moments. We derive the exact distribution of the likelihood ratio tests of homogeneity and simple hypothesis on the tail index of a two-parameter Pareto model. Such exact tests support the assessment of the performance of estimators. In particular, we discuss some problems that one can encounter when misemploying the log-normal assumption based methods supported by the Basel II framework. Real data and simulated examples illustrate the methods. (en)
Title
  • On the Favorable Estimation for Fitting Heavy Tailed Data
  • On the Favorable Estimation for Fitting Heavy Tailed Data (en)
skos:prefLabel
  • On the Favorable Estimation for Fitting Heavy Tailed Data
  • On the Favorable Estimation for Fitting Heavy Tailed Data (en)
skos:notation
  • RIV/67985807:_____/10:00342150!RIV11-AV0-67985807
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika
  • 3
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 276863
http://linked.open...ai/riv/idVysledku
  • RIV/67985807:_____/10:00342150
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • heavy-tailed distribution; exact likelihood ratio test; T-score moment estimator; insurance; Basel II (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [C9E3A1CC9217]
http://linked.open...i/riv/nazevZdroje
  • Computational Statistics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 25
http://linked.open...iv/tvurceVysledku
  • Fabián, Zdeněk
  • Stehlík, M.
  • Potocký, R.
  • Waldl, H.
http://linked.open...ain/vavai/riv/wos
  • 000280074100008
http://linked.open...n/vavai/riv/zamer
issn
  • 0943-4062
number of pages
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