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Penalized functional regression using R package PFLR.

Rob Cameron1, Tianyu Guan2, Haolun Shi1

  • 1Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, Canada.

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|September 15, 2025
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Summary
This summary is machine-generated.

Penalized functional regression models truncated coefficient functions, where predictors influence responses up to a cutoff point. The R package PFLR provides advanced methods for these models, demonstrated with simulations and real-world data.

Keywords:
B-spline basis functionsfunctional data analysisfunctional linear regressionpenalized B-splinespenalized regression

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Functional regression models effects where coefficient functions are truncated.
  • Truncated coefficient functions occur when functional predictors influence responses only up to a specific time point.
  • Penalized methods are crucial for estimating such models accurately.

Purpose of the Study:

  • Introduce the R package PFLR for penalized functional regression.
  • Provide a suite of methods for estimating models with truncated coefficient functions.
  • Demonstrate the package's utility through simulations and a real-world application.

Main Methods:

  • Implemented four distinct penalized functional regression methods within the PFLR package.
  • Utilized simulations to evaluate the performance of the implemented methods.
  • Applied the methods to analyze particulate matter emissions data.

Main Results:

  • The PFLR package offers versatile tools for advanced functional regression.
  • Simulations confirmed the effectiveness of the implemented methods for truncated coefficient functions.
  • The application to particulate matter data showcased practical utility.

Conclusions:

  • The PFLR package effectively addresses functional regression with truncated coefficient functions.
  • It provides robust methods for estimation, visualization, and interpretation.
  • The package is a valuable resource for researchers in functional data analysis.