A new bias-corrected estimator method in extreme value distributions with small sample size

Abstract

This paper proposes a bias-corrected expression for maximum likelihood estimators using the sequential number-theoretic method for optimization (SNTO) to improve the efficiency and accuracy of the estimators in three extreme value distributions (EVDs). It is well known that the widely used maximum likelihood estimation (MLE) could be often biased for small-size samples in EVDs. Meanwhile, numerical simulation results reveal that maximum likelihood estimators are suffered from high variance when the sample size is small and the impact is non-negligible. A comprehensive comparison study which includes classical bias-corrected methods and more recent ones is presented. Based on the simulation studies, the bias-correction estimator via SNTO is highly recommended to reduce the bias and variance of estimators. In addition, a real data set is illustrated to employ different techniques.

Keywords:

• Bias correction
• extreme value distribution
• maximum likelihood estimation
• monte carlo simulation
• sequential number-theoretic algorithm

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by UIC research grants [R201912, R202010] and Guangdong Higher Education Upgrading Plan (2021-2025) [grant number R0400001-22] and Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College (UIC) [grant number 2022B1212010006].