We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those estimated functions are more challenging in models with infinite-dimensional covariates than in regression models with scalar or vector-valued covariates due to a slower rate of convergence of the parameter estimators. Yet the suggested change point test is asymptotically distribution-free and consistent for one-change point alternatives. In the latter case we also show consistency of a change point estimator.

翻译：本文考虑响应变量为标量、协变量来自可分希尔伯特空间的线性模型。基于序贯残差经验分布函数，旨在检测误差分布中的变点。由于参数估计量的收敛速度较慢，与标量或向量值协变量的回归模型相比，在无限维协变量模型中这些估计函数的展开更具挑战性。然而，所提出的变点检验对于单变点备择假设是渐近分布自由且一致的。在后一种情况下，我们还证明了变点估计量的一致性。