Inference in a generalized endpoint-inflated binomial regression model

Generalized endpoint-inflated binomial regression was recently proposed to model count data with large frequencies of both zeros and right-endpoints. Maximum likelihood estimation (MLE) was developed for this model and simulations suggest that the resulting estimates behave well. However, large-sample properties of the MLE have not yet been rigorously established. Such results are however essential for ensuring reliable statistical inference and decision-making. This paper addresses this issue. Identifiability of the generalized endpoint-inflated binomial regression model is first proved. Then, consistency and asymptotic normality of the MLE are established. A simulation study is conducted to assess finite-sample behaviour of the estimator.