0642808 20260226074120.520251209235959.9 105005517502 001489380800001 10.1080/07474946.2025.2498933 26 s. P cav_un_epca*02905970747-4946443 (2025)350-326 neural networks quantiles regression outliers sequential example selection robust statistics cav_un_auth*0345793 Kalina Jan UTIA-B Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics Ústav teorie informace a automatizace AV ČR, v. v. i. https://www.tandfonline.com/doi/full/10.1080/07474946.2025.2498933 GA24-10078S GA ČR CZ cav_un_auth*0472835 Regression quantiles provide a flexible framework for modeling the conditional distribution of a response variable by estimating different parts of its distribution, thereby offering valuable insights into the relationship between predictors and outcomes. However, existing nonlinear regression quantile methods may be sensitive to the presence of severe outliers in the data. This paper starts with investigating robust versions of neural networks. The study includes a proposal of a sequential outlier detection procedure based on sequential example selection for robust neural networks. Further, robust quantile estimators for nonlinear regression is introduced. The proposed quantiles are inspired by least weighted squares regression. To enhance robustness to outliers, they assign implicit weights to individual samples and are specifically tailored for multilayer perceptrons, radial basis function networks, and regularized networks. Numerical experiments demonstrate that the robust quantiles improve generalization and outlier resistance. Simulations confirm that the proposed method outperforms traditional (non-robust) quantiles. WOS IN 10000 10200 10201 2026 RVO:67985556 https://hdl.handle.net/11104/0372665 S C STATISTICS&PROBABILITY 0.7 0 12.4 0.00028 0.28 372 26 0.468 30.39 0.78 60 Q2 0.500 18 Q4 15.1 0.38 Q4 15.1 2025 105005517502 SCOPUS PUBMED 001489380800001 WOS cav_un_epca*0290597 Sequential Analysis 44 3 2025 350 326 0747-4946 1532-4176