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An Algorithm of Nonparametric Quantile Regression.

Mei Ling Huang¹, Yansan Han¹, William Marshall¹

¹Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1 Canada.

Journal of Statistical Theory and Practice

|April 4, 2023

Summary

This summary is machine-generated.

This study introduces a new nonparametric quantile regression method to accurately predict extreme events. The novel approach overcomes limitations of linear methods, improving high quantile estimation and avoiding logically inconsistent results.

Keywords:

Conditional quantile Extreme value distribution Generalized Pareto distribution Kernel estimation Linear programming Nonparametric quantile regression

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Area of Science:

Statistics
Econometrics
Data Science

Background:

Extreme events significantly impact social and ecological systems.
Quantile regression is crucial for predicting these events across various fields.
Linear quantile regression faces challenges in estimating high quantiles and avoiding curve crossing.

Purpose of the Study:

Propose a novel nonparametric quantile regression method.
Address the limitations of linear quantile regression in estimating high conditional quantiles.
Develop a robust method for predicting extreme events.

Main Methods:

Introduced a nonparametric quantile regression approach.
Developed a three-step computational algorithm for estimation.
Derived asymptotic properties of the proposed estimator.

Main Results:

The proposed nonparametric method is more efficient than linear quantile regression.
Successfully estimated high conditional quantiles, overcoming curve crossing issues.
Demonstrated applicability through real-world examples including COVID-19 and blood pressure data.

Conclusions:

The novel nonparametric method offers improved accuracy for predicting extreme events.
This approach provides a more reliable tool for analyzing high quantiles in nonlinear scenarios.
The method has practical implications for fields dealing with extreme event prediction.