Nonparametric Bootstrap Confidence Intervals for High-Quantiles of Heavy-Tailed Distributions

2018 ◽  
Author(s):  
Svetlana Litvinova ◽  
Mervyn Joseph Silvapulle
Keyword(s):  
Confidence Intervals ◽  
Nonparametric Bootstrap ◽  
Bootstrap Confidence Intervals ◽  
Heavy Tailed Distributions ◽  
High Quantiles ◽  
Heavy Tailed

scholarly journals A Method for Confidence Intervals of High Quantiles

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 70
Author(s):  
Mei Ling Huang ◽  
Xiang Raney-Yan
Keyword(s):  
Confidence Intervals ◽  
Computational Algorithm ◽  
Geometric Mean ◽  
Asymptotic Properties ◽  
Quantile Estimation ◽  
Heavy Tailed Distributions ◽  
High Quantiles ◽  
High Quantile ◽  
Heavy Tailed ◽  
Infinite Moments

The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.

Generalized Bootstrap Confidence Intervals for High Quantiles

2010 ◽  
pp. 877-913
Author(s):  
Bin Wang ◽  
Satya Mishra ◽  
Madhuri Mulekar ◽  
Nutan Mishra ◽  
Kun Huang
Keyword(s):  
Confidence Intervals ◽  
Bootstrap Confidence Intervals ◽  
High Quantiles
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