A unified view of multitaper multivariate spectral estimation
A unified view of multitaper multivariate spectral estimation
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DOI：
10.1093/biomet/87.4.767
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发表时间：
2000-12-01
期刊：
影响因子：
2.7
通讯作者：
Walden, AT
中科院分区：
文献类型：
--
作者：
Walden, AT
交叉谱估计的正交多锥度框架为确定相应的统计性质提供了一个简单的统一结构。在这里，交叉谱估计由正交锥形交叉周期图的加权平均值表示，其权重对应于一组重新缩放的特征值。这种结构不仅包括使用Slepian和正弦锥的Thomson估计器，还包括Welch的加权重叠段平均估计器和包含频率平均交叉周期图的滞后窗估计器。这些估计量的均值、平滑和泄漏偏差、方差和渐近分布都可以用一种共同的方式表示；对固定数量的自由度进行比较。估计量的共同结构也为估计的交叉谱矩阵的可逆性提供了一个必要条件，即以双线性形式表示的估计量的权矩阵的秩必须大于或等于交叉谱矩阵的维数。给出了一个例子，说明了小泄漏的重要性，从而说明了在实践中各种估计器不必等效。
The orthogonal multitaper framework for cross-spectral estimators provides a simple unifying structure for determining the corresponding statistical properties. Here cross-spectral estimators are represented by a weighted average of orthogonally-tapered cross-periodograms, with the weights corresponding to a set of rescaled eigenvalues. Such a structure not only encompasses the Thomson estimators, using Slepian and sine tapers, but also Welch's weighted overlapped segment averaging estimator and lag window estimators including frequency-averaged cross-periodograms. The means, smoothing and leakage biases, variances and asymptotic distributions of such estimators can all be formulated in a common way; comparisons are made for a fixed number of degrees of freedom. The common structure of the estimators also provides a necessary condition for the invertibility of an estimated cross-spectral matrix, namely that the weight matrix of the estimator written in bilinear form must have rank greater than or equal to the dimension of the cross-spectral matrix. An example is given showing the importance of small leakage and thus illustrating that the various estimators need not be equivalent in practice.