Abstract:
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In this presentation we outline a new approach to perform spectral density estimation for subject- or trial-replicated time series by means of a flexible functional mixed-effects model. Replicate-specific spectral densities are modeled as random curves varying around a deterministic population-mean spectrum, where the variability of the replicate-specific curves is not assumed to be diagonal, i.e. there may exist explicit correlation between different replicate-specific curves in the population. By projecting the replicate-specific curves onto an orthonormal wavelet basis, estimation and prediction is carried out under an equivalent linear mixed-effects model in the wavelet coefficient domain. We give some insights into the finite-sample performance and the asymptotic properties of the developed estimators, which are based on a combination of classical linear mixed model methods and non-linear wavelet thresholding. Through several simulated data examples and a real brain-signal data example we highlight the influence of the correlation between different replicate-specific spectra, as this is among the innovations of our approach.
This is joint work with Rainer von Sachs.
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