Title :

Estimation of the intensity parameter of the germ-grain Quermass-interaction model when the number of germs is not observed

Author(s) :

Dereudre, David [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Lavancier, Frédéric [Auteur]
Helisova Stankova, Katerina [Auteur]

Journal title :

Scandinavian Journal of Statistics

Pages :

1-21

Publisher :

Wiley

Publication date :

2014

ISSN :

0303-6898

English keyword(s) :

Gibbs Point Process
germ-grain model
Quermass-Interaction Process
Area-interaction Process
Perimeter-interaction Process
Takacs-Fiksel estimator.
Takacs-Fiksel estimator

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Théorie [stat.TH]

English abstract : [en]

The Quermass-interaction model allows to generalise the classical germ-grain Boolean model in adding a morphological interaction between the grains. It enables to model random structures with specific morphologies which ...
Show more >The Quermass-interaction model allows to generalise the classical germ-grain Boolean model in adding a morphological interaction between the grains. It enables to model random structures with specific morphologies which are unlikely to be generated from a Boolean model. The Quermass-interaction model depends in particular on an intensity parameter, which is impossible to estimate from classical likelihood or pseudo-likelihood approaches because the number of points is not observable from a germ-grain set. In this paper, we present a procedure based on the Takacs-Fiksel method which is able to estimate all parameters of the Quermass-interaction model, including the intensity. An intensive simulation study is conducted to assess the efficiency of the procedure and to provide practical recommendations. It also illustrates that the estimation of the intensity parameter is crucial in order to identify the model. The Quermass-interaction model is finally fitted by our method to P. Diggle's heather dataset.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL