Extreme value index estimator using maximum likelihood and moment estimation

ABSTRACT

When a distribution function is in the max domain of attraction of an extreme value distribution, its tail can be well approximated by a generalized Pareto distribution. Based on this fact we use a moment estimation idea to propose an adapted maximum likelihood estimator for the extreme value index, which can be understood as a combination of the maximum likelihood estimation and moment estimation. Under certain regularity conditions, we derive the asymptotic normality of the new estimator and investigate its finite sample behavior by comparing with several classical or competitive estimators. A simulation study shows that the new estimator is competitive with other estimators in view of average bias, average MSE, and coefficient of variance of the new device for the optimal selection of the threshold.

KEYWORDS:

• Asymptotic normal distribution
• Domain of attraction
• Generalized Pareto distribution
• Maximum likelihood estimator
• Moment estimator.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 60G70; Secondary: 62G32

Funding

The first author was supported by a grant of the Swiss National Science Foundation. The second author was supported by NNSFC Grant 11171074.