Abstract:
In order to analyze random set processes, it is necessary to have simple statistics that can be used to describe their outcomes. The cumulants and several other parameters can be used for this purpose, but their estimates can be excessively variable if the most straightforward estimators are used. Through exploitation of similarities between this estimation problem and a similar one for a point process statistic, two modifications are suggested. Clear analytical results concerning the effects of these modifications were found through use of a specialized asymptotic regime, whose form was related to certain geometrical aspects of the modifications. Simulation results established that the modifications were highly effective at reducing estimator standard deviations for several Boolean models. The results suggested that the reductions in variance resulted from a balanced use of information in estimation of first and second moments, through eliminating the use of observations that were not used in second moment estimation.
Keywords:
random set, germ-grain models, cumulants, edge effects AMS Classification Numbers: 62M30 (primary), 60D05 (secondary)
tr89.pdf