A note on testing separability in spatial-temporal marked point processes.
In environmental risk analysis, it is common to assume the stochastic independence (or separability) between the marks associated with the random events of a spatial-temporal point process. Schoenberg (2004, Biometrics 60, 471-481) proposed several test statistics for this hypothesis and used simulated data to evaluate their performance. He found that a Cramér-von Mises-type test is powerful to detect gradual departures from separability although it is not uniformly powerful over a large class of alternative models. We present a semiparametric approach to model alternative hypotheses to separability and derive a score test statistic. We show that there is a relationship between this score test and some of the test statistics proposed by Schoenberg. Specifically, all are different versions of weighted Cramér-von Mises-type statistics. This gives some insight into the reasons for the similarities and differences between the test statistics' performance. We also point out some difficulties in controlling the type I error probability in Schoenberg's residual test.
Assunção
Renato
R
LESTE-Laboratório de Estatística Espacial, Departmento de Estatística, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG, Brazil. assuncao@est.ufmg.br
Maia
Alexandra
A
D001699:Biometry / Q000379:methods; D015233:Models, Statistical; D016012:Poisson Distribution; D015203:Reproducibility of Results