Pairwise likelihood estimation for multivariate mixed Poisson models generated by Gamma intensities

Florent Chatelain (1, 2) , Sophie Lambert-Lacroix (3) , Jean-Yves Tourneret (1, 4)

1 IRIT-SC - Signal et Communications
2 TéSA - Télécommunications Spatiales et Aéronautiques - Telecommunications for Space ant Aeronautics
3 SMS - Statistique et Modélisation Stochatisque
4 Toulouse INP - Institut National Polytechnique (Toulouse)

Estimating the parameters of multivariate mixed Poisson models is an important problem in image processing applications, especially for active imaging or astronomy. The classical maximum likelihood approach cannot be used for these models since the corresponding masses cannot be expressed in a simple closed form. This paper studies a maximum pairwise likelihood approach to estimate the parameters of multivariate mixed Poisson models when the mixing distribution is a multivariate Gamma distribution. The consistency and asymptotic normality of this estimator are derived. Simulations conducted on synthetic data illustrate these results and show that the proposed estimator outperforms classical estimators based on the method of moments. An application to change detection in low-flux images is also investigated.

Mots clés: Negative multinomial distributions; Pairwise likelihood estimation; Multivariate mixed Poisson models; Multivariate Gamma distributions

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Florent Chatelain, Sophie Lambert-Lacroix, Jean-Yves Tourneret. Pairwise likelihood estimation for multivariate mixed Poisson models generated by Gamma intensities. Statistics and Computing, 2009, 19 (3), pp.283-301. ⟨10.1007/s11222-008-9092-9⟩. ⟨hal-00853135⟩