TESTING THE HYPOTHESIS THAT A POINT PROCESS IS POISSON

The testing of the hypothesis that a point process is Poisson against a one-dimensional alternative is considered. The locally optimal test statistic is expressed as an infinite series of uncorrelated terms. These terms are shown to be asymptotically equivalent to terms based on the various orders of cumulant spectra. The efficiency of tests based on partial sums of these terms is found. ASYMPTOTIC EFFICIENCY; CUMULANT; CUMULANT SPECTRA; LOCAL EFFICIENCY; LOCAL OPTIMALITY; PERIODOGRAM; POINT PROCESS; POISSON PROCESS