A unified view of multitaper multivariate spectral estimation
Andrew T. Walden · Biometrika · 2000
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.