论文标题
在功能时间序列的二阶动力学中相关差异的关键测试
Pivotal tests for relevant differences in the second order dynamics of functional time series
论文作者
论文摘要
由于需要在统计上量化现代（复杂）数据集之间的差异的动机，这通常会导致随机过程的高分辨率测量在连续体中变化，因此我们提出了新颖的测试程序，以检测两个功能时间序列的二阶动力学之间的相关差异。为了考虑到表征这种功能数据的功能间动力学，采用了频域方法。开发了测试统计数据是为了比较光谱密度算子和相关特征元素中编码的主要变化模式的差异。在轻度的力矩条件下，我们显示了基本统计数据与布朗动议的收敛性并构建关键测试统计。后者是必不可少的，因为滋扰参数可能是笨拙的，并且它们的稳健估计是不可行的，尤其是在两个功能时间序列依赖的情况下。除了这些新颖的特征外，测试的特性对于任何选择频带的选择都具有鲁棒性，还可以以单个频率比较能量内容物。通过仿真研究验证了测试的有限样本性能，并使用fMRI数据的应用进行了说明。
Motivated by the need to statistically quantify differences between modern (complex) data-sets which commonly result as high-resolution measurements of stochastic processes varying over a continuum, we propose novel testing procedures to detect relevant differences between the second order dynamics of two functional time series. In order to take the between-function dynamics into account that characterize this type of functional data, a frequency domain approach is taken. Test statistics are developed to compare differences in the spectral density operators and in the primary modes of variation as encoded in the associated eigenelements. Under mild moment conditions, we show convergence of the underlying statistics to Brownian motions and construct pivotal test statistics. The latter is essential because the nuisance parameters can be unwieldy and their robust estimation infeasible, especially if the two functional time series are dependent. In addition to these novel features, the properties of the tests are robust to any choice of frequency band enabling also to compare energy contents at a single frequency. The finite sample performance of the tests are verified through a simulation study and are illustrated with an application to fMRI data.
