An Investigation of Quantile Function Estimators Relative to Quantile Confidence Interval Coverage

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Traditional quantile function estimators face limitations in accurately estimating extreme tails, especially with finite sample sizes.
• Accurate estimation of extreme quantiles is crucial for risk management, financial modeling, and outlier detection.

Purpose of the Study:

• To introduce a novel class of semi-parametric tail-extrapolated quantile estimators.
• To evaluate the performance of these new estimators, particularly in estimating extreme tails with limited data.
• To develop and compare methods for confidence interval estimation for quantile estimators.

Main Methods:

• Development of semi-parametric tail-extrapolated quantile estimators.
• Application of smoothed bootstrap and direct density estimation via characteristic function for confidence intervals.
• Comprehensive simulation studies to compare various quantile estimators and confidence interval methods.

Main Results:

• The proposed semi-parametric tail-extrapolated quantile estimators exhibit excellent performance in estimating extreme tails with finite sample sizes.
• Simulation results highlight the superiority of the new estimators over traditional methods.
• Guidance is provided on selecting the preferred quantile estimator and confidence interval method based on specific circumstances.

Conclusions:

• The semi-parametric tail-extrapolated quantile estimators offer a significant advancement for researchers dealing with extreme tail estimations.
• These estimators are a slight modification of traditional methods, making them accessible and appealing to a broad research audience.
• The developed confidence interval estimation methods enhance the reliability of extreme quantile estimates.