Application of Tempered Stable Distributions to the EEG-sleep Study of Neonates

• Activity Number: 526
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Alexandra Piryatinska*+
• Companies: San Francisco State University
• Keywords: levy processes ; tempered stable processes ; numerical MLE ; EEG-sleep data

Abstract

Smoothly Truncated Levy Processes were introduced by Koponen (1995). Rosinski (2007) studied the more general class of processes of similar type which he called tempered stable processes. A tempered stable process combines both the a-stable and Gaussian trends. In our study we consider symmetric Tempered Stable (TS) distributions and processes. TS distributions is described via characteristic functions and there is no closed form for the density functions. In our study we developed numerical Maximum Likelihood Estimates (MLE) for them. The above method was applied to a study of EEG-sleep signals of neonates. The EEG-sleep data are not stationary. Neurophysiologists have traditionally identified four distinct EEG patterns during sleep which we aggregated to just two sleep stages: active and quiet. At first we separated the time series into quasi-stationary increments using the change point detection algorithm. For the homogeneous increments the numerical MLE for symmetric TS distributions was applied. The conclusion is that the TS model is appropriate for distributions appearing in EEG-sleep signals for full-term and preterm babies.