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