  Understanding the seizure initiation process and its propagation pattern(s)
is a critical task in epilepsy research. Characteristics of the pre-seizure
electroencephalograms (EEGs) such as oscillating powers and high-frequency
activities are believed to be indicative of the seizure onset and spread
patterns. In this article, we analyze epileptic EEG time series using
nonparametric spectral estimation methods to extract information on
seizure-specific power and characteristic frequency [or frequency band(s)].
Because the EEGs may become nonstationary before seizure events, we develop
methods for both stationary and local stationary processes. Based on penalized
Whittle likelihood, we propose a direct generalized maximum likelihood (GML)
and generalized approximate cross-validation (GACV) methods to estimate
smoothing parameters in both smoothing spline spectrum estimation of a
stationary process and smoothing spline ANOVA time-varying spectrum estimation
of a locally stationary process. We also propose permutation methods to test if
a locally stationary process is stationary. Extensive simulations indicate that
the proposed direct methods, especially the direct GML, are stable and perform
better than other existing methods. We apply the proposed methods to the
intracranial electroencephalograms (IEEGs) of an epileptic patient to gain
insights into the seizure generation process.
