Some results on estimation of the tail index of a distribution

Jiazhu Pan

Research output: Contribution to journal › Article

3 Citations (Scopus)

Abstract

The author obtains the rate of strong convergence, mean squared error and optimal choice of the “smoothing parameter” (the sample fraction ) of a tail index estimator which was proposed by the author from Pickands’ estimator, and called modified Pickands’ estimator. The similar results about Hill’s estimator are also obtained, which generalize the corresponding results in [8,9]. Besides, some comparisons between Hill’s estimator and the modified Pickands’ estimator are given.
LanguageEnglish
Pages239-248
Number of pages10
JournalChinese Annals of Mathematics, Series B
Volume19 B
Issue number2
Publication statusPublished - 1998

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Tail Index
Estimator
Smoothing Parameter
Strong Convergence
Mean Squared Error
Generalise

Keywords

  • tail index
  • parameter estimation
  • strong convergence
  • mean squared error
  • comparisons of estimators

Cite this

Pan, Jiazhu. / Some results on estimation of the tail index of a distribution. In: Chinese Annals of Mathematics, Series B. 1998 ; Vol. 19 B, No. 2. pp. 239-248.
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Pan, J 1998, 'Some results on estimation of the tail index of a distribution' Chinese Annals of Mathematics, Series B, vol. 19 B, no. 2, pp. 239-248.

Some results on estimation of the tail index of a distribution. / Pan, Jiazhu.

In: Chinese Annals of Mathematics, Series B, Vol. 19 B, No. 2, 1998, p. 239-248.

Research output: Contribution to journal › Article

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AB - The author obtains the rate of strong convergence, mean squared error and optimal choice of the “smoothing parameter” (the sample fraction ) of a tail index estimator which was proposed by the author from Pickands’ estimator, and called modified Pickands’ estimator. The similar results about Hill’s estimator are also obtained, which generalize the corresponding results in [8,9]. Besides, some comparisons between Hill’s estimator and the modified Pickands’ estimator are given.

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KW - parameter estimation

KW - strong convergence

KW - mean squared error

KW - comparisons of estimators

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Pan J. Some results on estimation of the tail index of a distribution. Chinese Annals of Mathematics, Series B. 1998;19 B(2):239-248.

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