Estimating the first- and second-order parameters of a heavy-tailed distribution

Liang Peng, Yongcheng Qi

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

This paper suggests censored maximum likelihood estimators for the first- and second-order parameters of a heavy-tailed distribution by incorporating the second-order regular variation into the censored likelihood function. This approach is different from the bias-reduced maximum likelihood method proposed by Feuerverger and Hall in 1999. The paper derives the joint asymptotic limit for the first- and second-order parameters under a weaker assumption. The paper also demonstrates through a simulation study that the suggested estimator for the first-order parameter is better than the estimator proposed by Feuerverger and Hall although these two estimators have the same asymptotic variances.

Original languageEnglish (US)
Pages (from-to)305-312
Number of pages8
JournalAustralian and New Zealand Journal of Statistics
Volume46
Issue number2
DOIs
StatePublished - Jun 2004

Keywords

  • Bias
  • Censored likelihood function
  • Hill estimator
  • Second-order regular variation
  • Tail index

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