Robust functional logistic regression

Berkay Akturk (), Ufuk Beyaztas (), Han Lin Shang () and Abhijit Mandal ()
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Berkay Akturk: Marmara University
Ufuk Beyaztas: Marmara University
Han Lin Shang: Macquarie University
Abhijit Mandal: University of Texas at El Paso

Advances in Data Analysis and Classification, 2025, vol. 19, issue 1, No 6, 145 pages

Abstract: Abstract Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are sensitive to outliers, which may lead to inaccurate parameter estimates and inferior classification accuracy. We propose a robust estimation procedure for functional logistic regression, in which the observations of the functional predictor are projected onto a set of finite-dimensional subspaces via robust functional principal component analysis. This dimension-reduction step reduces the outlying effects in the functional predictor. The logistic regression coefficient is estimated using an M-type estimator based on binary response and robust principal component scores. In doing so, we provide robust estimates by minimizing the effects of outliers in the binary response and functional predictor variables. Via a series of Monte-Carlo simulations and using hand radiograph data, we examine the parameter estimation and classification accuracy for the response variable. We find that the robust procedure outperforms some existing robust and non-robust methods when outliers are present, while producing competitive results when outliers are absent. In addition, the proposed method is computationally more efficient than some existing robust alternatives.

Keywords: Bianco and Yohai estimator; Functional data; Functional principal component analysis; Logistic regression; 62G35; 62H30; 62H35 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11634-023-00577-z

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