Title: Sequential Detection of Three-Dimensional Signals under Dependent Noise,
Abstract: We study detection methods for multivariable signals under dependent noise.
The main focus is on three-dimensional signals, i.e. on signals in the
space-time domain. Examples for such signals are multifaceted. They include
geographic and climatic data as well as image data, that are observed over a
fixed time horizon. We assume that the signal is observed as a finite block of
noisy samples whereby we are interested in detecting changes from a given
reference signal. Our detector statistic is based on a sequential partial sum
process, related to classical signal decomposition and reconstruction
approaches applied to the sampled signal. We show that this detector process
converges weakly under the no change null hypothesis that the signal coincides
with the reference signal, provided that the spatial-temporal partial sum
process associated to the random field of the noise terms disturbing the
sampled signal con- verges to a Brownian motion. More generally, we also
establish the limiting distribution under a wide class of local alternatives
that allows for smooth as well as discontinuous changes. Our results also cover
extensions to the case that the reference signal is unknown. We conclude with
an extensive simulation study of the detection algorithm.