The paper concerns inference in the ill-conditioned functional response model, which is a part of functional data analysis. In this regression model, the functional response is modeled using several independent scalar variables. To verify linear hypotheses, we develop new test statistics by aggregating pointwise statistics using either integral or supremum. The new tests are scale-invariant, in contrast to the existing ones. To construct tests, we use different bootstrap methods. The performance of the new tests is compared with the performance of known tests through a simulation study and an application to a real data example.

翻译：本文关注病态函数响应模型中的推断问题，该模型属于函数数据分析范畴。在此回归模型中，函数响应通过若干独立标量变量进行建模。为验证线性假设，我们通过积分或上确界方法聚合逐点统计量，构建了新的检验统计量。与现有方法相比，新检验具有尺度不变性。在检验构建过程中，我们采用了不同的自助法。通过模拟研究和实际数据案例应用，将新检验的性能与已知检验进行了比较。