The limiting behavior of a modified maximal symmetric $2s$-spacing with applications

Abstract

This paper presents a solution to an open problem in astrophysics, namely that of estimating nonparametrically the strength of the pulsed signal in a series of high-energy photon arrival times. The newly proposed estimator, based on a modified maximal symmetric $2s$-spacing, is shown to be strongly consistent and asymptotically normally distributed, and a Monte Carlo study shows that its small and moderate sample behavior is very satisfactory. Additionally, new results regarding the weak and strong limiting behavior of modified maximal $2s$-spacings are derived.