On estimating the dependence between two point processes. (English) Zbl 0672.62088

Doss, Hani

Ann. Stat. 17, No. 2, 749-763 (1989).

Summary: To assess the dependence structure in a stationary bivariate point process the second-order distribution can be very useful. We prove that the natural estimates of this distribution, based on a realization \(A_ 1<A_ 2<...A_{n_ A}\), \(B_ 1<B_ 2<...<B_{n_ B}\) are asymptotically normal and we present a method for constructing approximate confidence intervals for this distribution.

MSC:

62M09	Non-Markovian processes: estimation
62M07	Non-Markovian processes: hypothesis testing
62E20	Asymptotic distribution theory in statistics
62G05	Nonparametric estimation
62G10	Nonparametric hypothesis testing

Keywords:

Ripley’s K-function; cross-intensity function; stationary; sequence; dependence structure; stationary bivariate point process; second-order distribution; asymptotically normal; approximate confidence intervals