ABSTRACT
The task of validly quantifying variations in electrical activity recorded when the brain is processing external or internal events is addressed. Three new statistical tests sensitive to different types of response changes, which test the null hypothesis that there is a homogeneous signal, are presented. In the case of latency jitter, the testing procedure was developed together with a procedure for estimating the unknown signal shifts. The tests provide a statistically valid and powerful tool in investigating signal variation, even with strong colored noise. Moreover, the differential sensitivity to different types of variations allows a study of the underlying signal variability even though the single signal cannot be estimated.
ABSTRACT
In this paper we derive the log likelihood function for point processes in terms of their stochastic intensities by using the martingale approach. For practical purposes we work with an approximate log likelihood function that is shown to possess the usual asymptotic properties of a log likelihood function. The resulting estimates are strongly consistent and asymptotically normal (under some regularity conditions). As a by-product, a strong law of large numbers and a central limit theorem for martingales in continuous times are derived.
