The Annals of Statistics

On Estimating the Dependence Between Two Point Processes

Hani Doss

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Abstract

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 $A_1 < A_2 < \cdots < A_{n_A}, B_1 < B_2 < \cdots < B_{n_B}$ are asymptotically normal and we present a method for constructing approximate confidence intervals for this distribution.

Article information

Source
Ann. Statist., Volume 17, Number 2 (1989), 749-763.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347140

Digital Object Identifier
doi:10.1214/aos/1176347140

Mathematical Reviews number (MathSciNet)
MR994265

Zentralblatt MATH identifier
0672.62088

JSTOR
links.jstor.org

Subjects
Primary: 62M09: Non-Markovian processes: estimation
Secondary: 62M07: Non-Markovian processes: hypothesis testing 62G05: Estimation 62G10: Hypothesis testing

Keywords
Bivariate point process Ripley's $K$-function cross-intensity function stationary point process stationary sequence

Citation

Doss, Hani. On Estimating the Dependence Between Two Point Processes. Ann. Statist. 17 (1989), no. 2, 749--763. doi:10.1214/aos/1176347140. https://projecteuclid.org/euclid.aos/1176347140


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