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

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 l...

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Bibliographic Details
Published in:Journal of statistical computation and simulation Vol. 92; no. 18; pp. 3862 - 3884
Main Authors: Wang, Sirao, Fang, Kai-Tai, Ye, Huajun
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 12.12.2022
Taylor & Francis Ltd
Subjects:
Bias
Bias correction
extreme value distribution
Extreme values
Maximum likelihood estimation
Maximum likelihood estimators
monte carlo simulation
Optimization
sequential number-theoretic algorithm
ISSN:0094-9655, 1563-5163
Online Access:Get full text
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Summary: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.
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ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2022.2085706