Robust functional linear regression models

Ufuk Beyaztas*, Han Lin Shang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

With advancements in technology and data storage, the availability of functional data whose sample observations are recorded over a continuum, such as time, wavelength, space grids, and depth, progressively increases in almost all scientific branches. The functional linear regression models, including scalar-on-function and function-on-function, have become popular tools for exploring the functional relationships between the scalar response-functional predictors and functional response-functional predictors, respectively. However, most existing estimation strategies are based on non-robust estimators that are seriously hindered by outlying observations, which are common in applied research. In the case of outliers, the non-robust methods lead to undesirable estimation and prediction results. Using a readily-available R package robflreg, this paper presents several robust methods build upon the functional principal component analysis for modeling and predicting scalar-on-function and function-on-function regression models in the presence of outliers. The methods are demonstrated via simulated and empirical datasets.

Original languageEnglish
Pages (from-to)212-233
Number of pages22
JournalR Journal
Volume15
Issue number1
DOIs
Publication statusPublished - Mar 2023

Keywords

  • Functional linear regression models
  • Function-on-function linear regression model
  • Functional principal component analysis
  • Robust estimation of the scalar-on-function linear regression model
  • Robust estimation of the function-on-function linear regression model

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