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 spatia...

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Bibliographic Details
Published in:Journal of the American Statistical Association 2010-06, Vol.105 (490), p.634-646
Main Authors: Freyermuth, Jean-Marc, Ombao, Hernando, von Sachs, Rainer
Format: Article
Language:English
Subjects:
Applications
Coefficients
Combinatorics
Combinatorics. Ordered structures
Confidence interval
Dyadics
Estimate reliability
Estimation methods
Estimators
Exact sciences and technology
Fourier analysis
General topics
Graph theory
Log-spectrum estimation
Mathematical analysis
Mathematical models
Mathematics
Mixed effects models
Panel time series
Population estimates
Probability and statistics
Recursive dyadic partitioning
Sciences and techniques of general use
Statistical methods
Statistical variance
Statistics
Theory and Methods
Threshing
Time series
Tree-structured wavelets
Waveform analysis
Wavelet transforms
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Summary: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.
ISSN:0162-1459
1537-274X
DOI:10.1198/jasa.2010.tm09132