MISE-OPTIMAL GROUPING OF POINT-PROCESS DATA WITH A CONSTANT DISPERSION RATIO

Given a set of point-process event times with constant dispersion ratio, we are interested in estimating the rate function by grouping the event times into count data from equal-width time intervals. We group in order to smooth the resulting piecewise-constant rate function using one of our two existing methods: I-SMOOTH and MNO-PQRS. Using the mean integrated squared error (MISE) for piecewise-constant rate functions, we create two estimators; minimizing the estimated MISE function yields the chosen number of intervals. The MISE function provides insights into the optimal number of intervals as a function of the rate-function shape and expected number of events. Across several examples, our two number-of-intervals estimators perform well and similarly; nevertheless, one dominates in terms of realized MISE value.