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Robust scalar-on-function partial quantile regression.

Ufuk Beyaztas1, Mujgan Tez1, Han Lin Shang2

  • 1Department of Statistics, Marmara University, Kadikoy-Istanbul, Turkey.

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|June 5, 2024
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Summary
This summary is machine-generated.

This study introduces a robust method for scalar-on-function quantile regression, effectively handling outliers and leverage points in functional data. The new approach ensures reliable parameter estimation and predictions, outperforming existing techniques.

Keywords:
Functional dataiteratively reweightingpartial quantile covariancerobust estimation

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Scalar-on-function quantile regression offers robustness to response outliers.
  • It remains vulnerable to leverage points in functional predictors, impacting model accuracy.
  • Leverage points can distort predictor matrix eigenstructures, leading to poor estimation.

Purpose of the Study:

  • To develop a robust procedure for scalar-on-function quantile regression.
  • To address challenges posed by both outliers and leverage points in functional predictors.
  • To ensure reliable parameter estimation and prediction in the presence of data anomalies.

Main Methods:

  • A functional partial quantile regression approach is proposed.
  • Weighted partial quantile covariance is introduced for component extraction.
  • Iterative reweighting of partial quantile components ensures robustness.

Main Results:

  • The proposed method demonstrates robust estimation and prediction performance.
  • Monte-Carlo experiments and an empirical example validate the approach.
  • Favorable comparisons were made against existing statistical methods.

Conclusions:

  • The novel method effectively handles outliers and leverage points in scalar-on-function quantile regression.
  • Reliable estimation and prediction are achieved even with contaminated functional data.
  • An R package, robfpqr, is available for practical implementation.