Statistics and Its Interface

Volume 11 (2018)

Number 3

Testing the zonal stationarity of spatial point processes: applied to prostate tissues and trees locations

Pages: 491 – 501



Azam Saadatjouy (Department of Statistics, Shahid Beheshti University, Tehran, Iran)

Ali Reza Taheriyoun (Department of Statistics, Shahid Beheshti University, Tehran, Iran)

Mohammad Q. Vahidi-Asl (Department of Statistics, Shahid Beheshti University, Tehran, Iran)


This work aims to test the second-order stationarity of a spatial point pattern based on the local spectra concept. Using a logarithmic transformation, the mechanism of the proposed test becomes approximately identical to a simple two factor analysis of variance with the known variance of the noise term. This procedure can be also used for testing the stationarity in the neighborhood of a particular point of the observation window. The same idea is used in post-hoc tests to cluster the point pattern into stationary and non-stationary sub-windows. The performance of the proposed method is examined through a simulation study and is then applied to a practical data. The proposed test shows a considerable empirical power and satisfactorily empirical size.


complete covariance density function, evolutionary periodogram, spatial point process, spectral density function, zonal stationarity

2010 Mathematics Subject Classification

Primary 60G55, 62M15. Secondary 62F15.

Received 28 January 2017

Published 17 September 2018