A Multitaper Frequency-Domain Bootstrap Method.

Spectral properties of the electroencephalogram (EEG) are commonly analyzed to characterize the brain's oscillatory properties in basic science and clinical neuroscience studies. The spectrum is a function that describes power as a function of frequency. To date inference procedures for spectra have focused on constructing confidence intervals at single frequencies using large sample-based analytic procedures or jackknife techniques. These procedures perform well when the frequencies of interest are chosen before the analysis. When these frequencies are chosen after some of the data have been analyzed, the validity of these conditional inferences is not addressed. If power at more than one frequency is investigated, corrections for multiple comparisons must also be incorporated. To develop a statistical inference approach that considers the spectrum as a function defined across frequencies, we combine multitaper spectral methods with a frequency-domain bootstrap (FDB) procedure. The multitaper method is optimal for minimizing the bias-variance tradeoff in spectral estimation. The FDB makes it possible to conduct Monte Carlo based inferences for any part of the spectrum by drawing random samples that respect the dependence structure in the EEG time series. We show that our multitaper FDB procedure performs well in simulation studies and in analyses comparing EEG recordings of children from two different age groups receiving general anesthesia.