Smoothness selection for penalized quantile regression splines.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Modern data analysis frequently requires fitting numerous nonparametric quantile regressions, particularly for constructing growth charts and identifying developmental biomarkers.
• Penalized spline smoothing is a common technique for these analyses, but reliable automatic selection of the smoothing parameter is critical for accuracy.

Purpose of the Study:

• To investigate the performance of smoothness selection methods in nonparametric quantile regression, especially when estimating extreme quantiles.
• To propose and evaluate improved methods for smoothing parameter selection in large-scale quantile regression analyses.

Main Methods:

• Evaluated two popular smoothness selection methods for penalized spline smoothing in nonparametric quantile regression.
• Proposed and assessed multifold cross-validation and a novel likelihood approach for smoothing parameter selection.
• Conducted a simulation study and applied the methods to functional magnetic resonance imaging (fMRI) data.

Main Results:

• Identified that two common smoothness selection methods can overfit when estimating extreme quantiles as a function of a predictor (e.g., age).
• Demonstrated that multifold cross-validation and the novel likelihood approach yield improved results compared to standard methods.
• The proposed methods showed favorable performance in both simulation and fMRI data applications.

Conclusions:

• Standard smoothness selection methods may be unreliable for estimating extreme quantiles in large-scale nonparametric regression.
• Multifold cross-validation and the novel likelihood approach offer more robust and accurate solutions for smoothing parameter selection.
• These improved methods are valuable for applications such as developmental biomarker identification and analysis of complex datasets like fMRI.