Robust scalar-on-function partial quantile regression

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.