Asymptotic properties of the maximum likelihood estimator in zero-inflated binomial regression

Alpha Oumar Diallo (1, 2, 3) , Aliou Diop (1) , Jean-François Dupuy (2, 3)

1 LERSTAD - laboratoire d'Etudes et de recherches en Statistiques et Développement
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 INSA Rennes - Institut National des Sciences Appliquées - Rennes

The zero-inflated binomial (ZIB) regression model was proposed to account for excess zeros in binomial regression. Since then, the model has been applied in various fields, such as ecology and epidemiology. In these applications, maximum-likelihood estimation (MLE) is used to derive parameter estimates. However, theoretical properties of the MLE in ZIB regression have not yet been rigorously established. The current paper fills this gap and thus provides a rigorous basis for applying the model. Consistency and asymptotic normality of the MLE in ZIB regression are proved. A consistent estimator of the asymptotic variance-covariance matrix of the MLE is also provided. Finite-sample behavior of the estimator is assessed via simulations. Finally, an analysis of a data set in the field of health economics illustrates the paper.

Mots clés: Asymptotic normality; consistency; count data; excess of zeros; simulations

Domaines: Statistiques [math.ST]

Alpha Oumar Diallo, Aliou Diop, Jean-François Dupuy. Asymptotic properties of the maximum likelihood estimator in zero-inflated binomial regression. Communications in Statistics - Theory and Methods, 2017, 46 (20), pp.9930-9948. ⟨10.1080/03610926.2016.1222437⟩. ⟨hal-01538370⟩