Robust Estimation of L 1 -Modal Regression Under Functional Single-Index Models for Practical Applications

Fatimah A. Almulhim, Mohammed B. Alamari, Salim Bouzebda (), Zoulikha Kaid and Ali Laksaci
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Fatimah A. Almulhim: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Mohammed B. Alamari: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
Salim Bouzebda: Laboratoire de Mathématiques Appliquées de Compiègne (L.M.A.C.), Université de Technologie de Compiègne, 60200 Compiègne, France
Zoulikha Kaid: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
Ali Laksaci: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia

Mathematics, 2025, vol. 13, issue 4, 1-20

Abstract: We propose a robust procedure to estimate the conditional mode of a univariate outcome O given a Hilbertian explanatory variable I , under the assumption that ( O , I ) follow a single-index structure. The estimator is constructed using the M -estimator for the conditional density, and we establish its complete convergence. We discuss the estimator’s advantages in addressing challenges within functional data analysis, particularly robustness and reliability. We then evaluate both the performance and practical implementation of our method via Monte Carlo simulations. Furthermore, we carry out an empirical study to showcase the improved reliability and robustness of this estimator compared to conventional approaches. In particular, our methodology is applied to predict fuel quality based on spectrometry data, illustrating its strong potential in real-world scenarios.

Keywords: functional data; functional M -regression; robust estimator; modal regression; kernel smoothing; conditional quantile; additive model; single-index model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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