Robust Estimation of L1-Modal Regression Under Functional Single-Index Models for Practical Applications

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.