Estimating the First and Second Order Parameters of a Heavy Tailed Distribution

We suggest 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 MLE proposed by Feuerverger & Hall (1999). In comparison with Feuerverger & Hall (1999), we derive the joint asymptotic limit for the first and second order parameters under a weaker assumption. We also demonstrate through a simulation study that our estimator for the first order parameter is better than that proposed by Feuerverger & Hall (1999) although these two estimators have the same asymptotic variances.