Robust spatial scalar-on-function regression: a Fisher-consistent redescending M-estimation approach
Environmental and Ecological Statistics, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s10651-026-00757-y
- Dergi Adı: Environmental and Ecological Statistics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, IBZ Online, ABI/INFORM, Aerospace Database, BIOSIS, Environment Index, Geobase, Greenfile, Zoological Record, Natural Science Collection (ProQuest), Biological Science Database (ProQuest), Biomedical Reference Collection: Corporate Edition (EBSCO), Earth, Atmospheric, & Aquatic Science Collection (ProQuest), Sociology Source Ultimate (EBSCO), Technology Collection (ProQuest)
- Anahtar Kelimeler: Bias-corrected estimating equations, Hybrid IRLS-Newton algorithm, Outliers, Robust functional principal components, Spatial autoregressive model
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
We develop a Fisher-consistent redescending robust estimator for the spatial scalar-on-function regression model, where a scalar response depends on both a functional predictor and a spatial autoregressive lag. Existing estimation procedures for this model are typically based on likelihood methods or monotone-loss robust M-estimators. They may be highly sensitive to vertical outliers, leverage points in the functional predictor, and numerical instability induced by strong spatial dependence. To address these issues, we propose a new estimation framework that first applies robust functional principal component analysis to obtain a contamination-resistant finite-dimensional representation of the functional predictor and then estimates the resulting spatial regression model through a bias-corrected system of M-estimating equations. The proposed method allows redescending loss functions, including Andrews’ sine and Danish losses, and jointly estimates the regression coefficients, spatial dependence parameter, and scale parameter within a unified Fisher-consistent framework. For computation, we develop a hybrid IRLS-Newton algorithm that combines weighted least-squares updates for the regression parameters with a Newton-Raphson update for the spatial parameter. We establish Fisher consistency, consistency, asymptotic normality, and the asymptotic distribution of the reconstructed slope function. Monte Carlo experiments show that the proposed estimators remain competitive under clean data and provide substantial robustness gains under contamination when the estimation algorithm converges. The results also indicate that severe contamination combined with strong spatial dependence may increase computational difficulty in highly challenging settings. An application to French air-quality data further demonstrates the practical usefulness of the proposed framework, yielding competitive predictive performance and reliable estimation of spatial dependence. Our method has been implemented in the fcsar R package.