A stable method for direct estimation of single-index terms in GAMs with an application to bike-sharing demand
Abstract
Single-index terms have been increasingly applied in generalized additive models (GAMs) across diverse areas due to their versatility in integrating functional flexibility with parametric dimension reduction while maintaining interpretability. However, the estimation presents severe computational challenges. This paper introduces a stable method based on Fisher scoring that dynamically updates the boundaries of the single-index covariates within a unified iterative framework using P-splines. Simulation studies with moderate sample sizes under non-Gaussian distributions confirm the empirical consistency of the estimation across multiple scenarios. Notably, the proposed method remains stable where state-of-the-art competitive methods fail to recover true single-index coefficients and their associated nonlinear functions, and is 80.13 times faster than the usual two-step method in the most computationally intensive scenario. The modeling advantage is illustrated through an application to Capital Bike Sharing data, where we deal with a single-index interaction effect for each year, with distinct single-index coefficients, a complex structure that makes competitive methods inapplicable. The proposed method is implemented in R, with all functions available at https://github.com/silva-danilo/sipgam for reproducibility and transparency in comparisons.
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BibTeX
@misc{silva2026stable,
title = {{A stable method for direct estimation of single-index terms in GAMs with an application to bike-sharing demand}},
author = {Danilo V. Silva and Gilberto A. Paula},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.21641},
eprint = {2605.21641},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.21641},
}
RIS
TY - UNPB
TI - A stable method for direct estimation of single-index terms in GAMs with an application to bike-sharing demand
AU - Danilo V. Silva
AU - Gilberto A. Paula
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2605.21641
UR - https://arxiv.org/abs/2605.21641
AB - Single-index terms have been increasingly applied in generalized additive models (GAMs) across diverse areas due to their versatility in integrating functional flexibility with parametric dimension reduction while maintaining interpretability. However, the estimation presents severe computational challenges. This paper introduces a stable method based on Fisher scoring that dynamically updates the boundaries of the single-index covariates within a unified iterative framework using P-splines. Simulation studies with moderate sample sizes under non-Gaussian distributions confirm the empirical consistency of the estimation across multiple scenarios. Notably, the proposed method remains stable where state-of-the-art competitive methods fail to recover true single-index coefficients and their associated nonlinear functions, and is 80.13 times faster than the usual two-step method in the most computationally intensive scenario. The modeling advantage is illustrated through an application to Capital Bike Sharing data, where we deal with a single-index interaction effect for each year, with distinct single-index coefficients, a complex structure that makes competitive methods inapplicable. The proposed method is implemented in R, with all functions available at https://github.com/silva-danilo/sipgam for reproducibility and transparency in comparisons.
ER -