We construct a goodness-of-fit test for the Functional Linear Model with Scalar Response (FLMSR) with responses Missing At Random (MAR). For that, we extend an existing testing procedure for the case where all responses have been observed to the case where the responses are MAR. The testing procedure gives rise to a statistic based on a marked empirical process indexed by the randomly projected functional covariate. The test statistic depends on a suitable estimator of the functional slope of the FLMSR when the sample has MAR responses, so several estimators are proposed and compared. With any of them, the test statistic is relatively easy to compute and its distribution under the null hypothesis is simple to calibrate based on a wild bootstrap procedure. The behavior of the resulting testing procedure as a function of the estimators of the functional slope of the FLMSR is illustrated by means of several Monte Carlo experiments. Additionally, the testing procedure is applied to a real data set to check whether the linear hypothesis holds.

翻译：在存在随机缺失响应的标量函数回归中的线性检验 翻译后的摘要： 我们构建了一个适用于存在随机缺失响应的标量函数线性模型回归（FLMSR）的拟合度检验。为此，我们将针对所有已观测到的响应的情况下已有的检验程序扩展到了响应为随机缺失的情况。测试程序产生的统计量基于被随机投影的函数协变量的标记经验过程。当样本具有MAR响应时，测试统计量取决于FLMSR的函数斜率的合适数估计器，因此提出并比较了几个估计器。使用其中任何一个估计器，测试统计量的计算相对容易，空假设下的分布易于根据野蛮引导过程进行校准。使用多个 Monte Carlo 实验说明了这种测试程序的行为对FLMSR的函数斜率估计器的影响。此外，将该测试程序应用于一个真实数据集以检查是否成立线性假设。