论文标题
功能线性回归中关键推断的RKHS方法
An RKHS approach for pivotal inference in functional linear regression
论文作者
论文摘要
我们开发了通过再现的内核希尔伯特空间方法来测试有关时间序列功能线性回归中斜率函数的假设的方法。与大多数文献考虑了斜率函数的确切无效测试的大多数文献相反，我们对零假设感兴趣，即斜率函数仅消失了大约消失，而相对于$ l^2 $ -Norm的偏差是偏差。提出了渐近关键测试，该测试不需要估计滋扰参数和长期协方差。证明我们方法的有效性的关键技术工具包括统一的巴哈杜尔表示和弱不变性原理，用于顺序估算斜坡函数的过程。考虑到标函数函数和功能在功能上的线性回归，并提供了实施我们方法的有限样本方法。我们还通过小型仿真研究和数据示例来说明我们方法的潜力。
We develop methodology for testing hypotheses regarding the slope function in functional linear regression for time series via a reproducing kernel Hilbert space approach. In contrast to most of the literature, which considers tests for the exact nullity of the slope function, we are interested in the null hypothesis that the slope function vanishes only approximately, where deviations are measured with respect to the $L^2$-norm. An asymptotically pivotal test is proposed, which does not require the estimation of nuisance parameters and long-run covariances. The key technical tools to prove the validity of our approach include a uniform Bahadur representation and a weak invariance principle for a sequential process of estimates of the slope function. Both scalar-on-function and function-on-function linear regression are considered and finite-sample methods for implementing our methodology are provided. We also illustrate the potential of our methods by means of a small simulation study and a data example.
