A Positive and Negative Integer-valued Bilinear Type Process

Alain Latour (1) , Lionel Truquet (2)

1 SMS - Statistique et Modélisation Stochatisque
2 CREST - Centre de Recherche en Économie et Statistique

With the aim of generalizing a bilinear type counting model, we redefine a more elaborated model than the one proposed by Doukhan et al. (2006). This new model, which can be useful in a context of inventory management or epidemiology, is based on a thinning operator allowing for negative values. In a simple way, we demonstrate the existence of such a process. The estimation of the parameters is tackled with the help of a quasi-maximum likelihood approach (referred to as QMLE). Under certain hypotheses, we prove that these QMLE estimators are strongly convergent. With some additionnal assumptions, we obtain asymptotically normal estimators

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

Alain Latour, Lionel Truquet. A Positive and Negative Integer-valued Bilinear Type Process. Joint meeting of the Statistical Society of Canada and the Société Française de Statistique, May 2008, Ottawa, Canada. ⟨hal-00851716⟩