ROBUSTNESS FOR INHOMOGENEOUS POISSON POINT PROCESSES

RENATO ASSUNÇÃO^{1} AND PETER GUTTORP^{2}

1Departamento de Estatística, UFMG, Caixa Postal 702, Belo Horizonte MG Brazil 30161-970, Brazil

2Department of Statistics, University of Washington, Seattle, WA 98195-1720, U.S.A.

(Received March 17, 1995; revised May 25, 1998)

Abstract. We consider robustness for estimation of parametric inhomogeneous Poisson point processes. We propose an influence functional to measure the effect of contamination on estimates. We also propose an M-estimator as an alternative to maximum likelihood estimator, show its consistency and asymptotic normality.

Key words and phrases: Robustness, influence function, M-estimator, point process, Poisson process.