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 substantially outperform classical and Huber-type robust competitors under contamination, particularly in severe outlier settings. An application to French air-quality data further demonstrates improved predictive performance and stable estimation of spatial dependence. Our method has been implemented in the fcsar R package.

翻译：针对空间标量对函数回归模型，我们发展了一种Fisher相合的回降鲁棒估计量。该模型中标量响应同时依赖于函数型预测变量和空间自回归滞后项。现有的估计方法通常基于似然方法或单调损失鲁棒M估计量，但可能对垂直异常值、函数型预测变量中的杠杆点以及强空间依赖引起的数值不稳定性高度敏感。为解决这些问题，我们提出一种新的估计框架：首先应用鲁棒函数主成分分析获得函数型预测变量的抗污染有限维表示，然后通过偏差校正的M估计方程系统估计所得的空间回归模型。所提方法允许使用回降损失函数（包括Andrews正弦损失和Danish损失），并在统一的Fisher相合框架内联合估计回归系数、空间依赖参数和尺度参数。计算方面，我们开发了一种混合IRLS-Newton算法，将回归参数的加权最小二乘更新与空间参数的Newton-Raphson更新相结合。我们建立了Fisher相合性、相合性、渐近正态性以及重建斜率函数的渐近分布。蒙特卡洛实验表明，所提估计器在清洁数据下保持竞争力，在污染数据下（尤其是严重异常值设置）显著优于经典及Huber型鲁棒竞争方法。法国空气质量数据的应用进一步展示了改进的预测性能和稳定的空间依赖性估计。该方法已在fcsar R包中实现。