This article studies global testing of the slope function in functional linear regression model in the framework of reproducing kernel Hilbert space. We propose a new testing statistic based on smoothness regularization estimators. The asymptotic distribution of the testing statistic is established under null hypothesis. It is shown that the null asymptotic distribution is determined jointly by the reproducing kernel and the covariance function. Our theoretical analysis shows that the proposed testing is consistent over a class of smooth local alternatives. Despite the generality of the method of regularization, we show the procedure is easily implementable. Numerical examples are provided to demonstrate the empirical advantages over the competing methods.

翻译：本文章研究在复制核心Hilbert空间的框架内对功能性线性回归模型中的斜度函数进行全球测试。 我们提议基于平稳性正规化估计值的新的测试统计。 测试统计的无症状分布是在无效假设下确定的。 显示无效无症状分布由再生产内核和共变函数共同确定。 我们的理论分析表明,提议的测试与平滑的本地替代方法一致。 尽管常规化方法很普遍,但我们显示程序很容易实施。 提供了数字实例,以证明对竞争方法的经验优势。