Multivariate spectral analysis using Cholesky decomposition
Multivariate spectral analysis using Cholesky decomposition
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DOI：
10.1093/biomet/91.3.629
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发表时间：
2004-09-01
期刊：
影响因子：
2.7
通讯作者：
Guo, WS
中科院分区：
文献类型：
--
作者：
Dai, M;Guo, WS
我们建议平滑的Cholesky分解的原始估计的多元光谱，允许不同程度的平滑不同的元素。最后的谱估计是由光滑的Cholesky元重构的，并且是一致的和正定的。更重要的是，频谱的Cholesky分解矩阵可以用作生成时间序列的传递函数，该时间序列的频谱与傅立叶频率处的给定频谱相同。这不仅为我们提供了很大的灵活性，在模拟中，但也允许我们通过使用Cholesky分解的谱估计生成自举样本来构建多变量谱的自举置信区间。一个数值例子和一个应用程序的脑电图数据被用作插图。
We propose to smooth the Cholesky decomposition of a raw estimate of a multivariate spectrum, allowing different degrees of smoothness for different elements. The final spectral estimate is reconstructed from the smoothed Cholesky elements, and is consistent and positive definite. More importantly, the Cholesky decomposition matrix of the spectrum can be used as a transfer function in generating time series whose spectrum is identical to the given spectrum at the Fourier frequencies. This not only provides us with much flexibility in simulations, but also allows us to construct bootstrap confidence intervals for the multivariate spectrum by generating bootstrap samples using the Cholesky decomposition of the spectral estimate. A numerical example and an application to electroencephalogram data are used as illustrations.