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Interval-valued scalar-on-function linear quantile regression based on the bivariate center and radius method.

Kaiyuan Liu1, Min Xu1, Jiang Du1,2

  • 1School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, People's Republic of China.

Journal of Applied Statistics
|July 4, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a robust interval-valued quantile regression model for analyzing complex big data. The new method offers more reliable results than traditional mean regression, especially with outliers.

Keywords:
46S2062-0862F10Interval-valued functional datafunctional variablesparametric estimationquantile regressionsymbolic data analysis

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Area of Science:

  • Statistics
  • Symbolic Data Analysis
  • Big Data Analytics

Background:

  • Interval-valued functional data are crucial for big data analysis.
  • Mean regression is common but sensitive to outliers.
  • Robust methods are needed for reliable interval-valued functional data analysis.

Purpose of the Study:

  • To propose a robust interval-valued scalar-on-function linear quantile regression model.
  • To address the limitations of mean regression in the presence of outliers.
  • To enhance the analysis of interval-valued functional data.

Main Methods:

  • Developed two linear quantile regression models using the bivariate center and radius method.
  • Applied the models to interval-valued responses and functional regressors.
  • Utilized numerical simulations and real-world climate data for validation.

Main Results:

  • The proposed interval-valued quantile regression model demonstrates increased robustness and efficiency.
  • The method outperforms traditional mean regression, particularly with outlier-prone data.
  • Effectiveness is validated through simulations and climate dataset analysis.

Conclusions:

  • The novel interval-valued quantile regression model provides a superior alternative to mean regression.
  • This method enhances the analysis of big data with interval-valued functional characteristics.
  • The findings are significant for researchers in statistics and data analysis.