Far East Journal of Theoretical Statistics
Volume 19, Issue 2, Pages 245 - 271
(July 2006)
|
|
CONSISTENT ESTIMATES OF THIRD-ORDER SPECTRAL DENSITY FUNCTION
OF A TATIONARY POINT PROCESS: APPLICATION TO NEUROPHYSIOLOGICAL PROBLEMS
V. G. Vassiliadis (Greece) and A. G. Rigas (Greece)
|
Abstract: In this paper, we discuss a way of
estimating the third-order spectral density function (sdf) of a discretized
stationary point process (spp). The estimate is based on the modified
third-order periodogram statistic, which is computed via the FFT algorithm. The
periodogram statistic is smoothed properly in order to achieve a consistent
estimate. The well-known method of periodogram smoothing using spectral windows
is combined with Welch’s smoothing approach (split-record method) and an
improved estimate is obtained. The asymptotic normality of the improved estimate
is proved under certain conditions and a comparison with
the
estimate
based
only on the Welch’s method is
made. Illustrative examples
using four data sets from the field of Neurophysiology are presented. |
Keywords and phrases: Fourier-Stieltjes transform, modified third-order periodogram,
Welch’s method, spectral window, asymptotic normality, Neurophysiological
examples. |
|
Number of Downloads: 256 | Number of Views: 936 |
|