We introduce and study a family of robust estimators for the functional logistic regression model whose robustness automatically adapts to the data thereby leading to estimators with high efficiency in clean data and a high degree of resistance towards atypical observations. The estimators are based on the concept of density power divergence between densities and may be formed with any combination of lower rank approximations and penalties, as the need arises. For these estimators we prove uniform convergence and high rates of convergence with respect to the commonly used prediction error under fairly general assumptions. The highly competitive practical performance of our proposal is illustrated on a simulation study and a real data example which includes atypical observations.

翻译：我们研究并引入了一族用于函数逻辑回归模型的鲁棒估计量，其鲁棒性可自动适应数据，从而在干净数据中实现高估计效率，并对异常观测值具有强抗性。该估计量基于密度之间的密度幂散度概念，并可根据需要结合任意低秩近似与惩罚项构建。在相当一般的假设下，我们证明了这些估计量相对于常用预测误差的一致收敛性与高收敛速率。通过模拟研究及包含异常观测值的真实数据实例，验证了所提方法在实践中的高度竞争力。