Tree-Structured Wavelet Estimation in a Mixed Effects Model for Spectra of Replicated Time Series

This article develops a method for estimating the spectrum of a stationary process using time series traces recorded from experimental designs. Our procedure estimates the "common" log-spectrum and the variability over the traces (or subjects) using a mixed effects model. We combine spatially adaptive smoothing methods with recursive dyadic partitioning to construct a model for predicting subject-specific effects. The method is easy to implement and can handle large datasets because it uses the discrete wavelet transform which is computationally efficient. Numerical studies confirm that the proposed method performs very well despite its simplicity. The method is also applied to a multisubject electroencephalogram dataset.