论文标题
基于RKHS的新型全局测试，用于功能线性模型
A new RKHS-based global testing for functional linear model
论文作者
论文摘要
本文研究了繁殖核希尔伯特空间的框架中功能线性回归模型中斜率函数的全局测试。我们根据平滑度正则估计器提出了一个新的测试统计量。测试统计量的渐近分布是在零假设下建立的。结果表明，无渐近分布是通过再现核和协方差函数共同确定的。我们的理论分析表明，在一类平滑的局部替代方案中，提出的测试是一致的。尽管正规化方法具有普遍性，但我们表明该过程很容易实现。提供了数值示例，以证明与竞争方法相对于竞争方法的经验优势。
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.
