Asymptotic properties in the Probit-Zero-inflated Binomial regression model

TL;DR

This paper develops a maximum likelihood estimation method for a zero-inflated Binomial regression model with a probit link, establishing its theoretical properties including existence, consistency, and asymptotic normality.

Contribution

It introduces a new estimation procedure for the ZIB model with probit link and proves its asymptotic properties, filling a gap in the theoretical understanding.

Findings

Establishment of existence of the estimator

Proof of consistency of the estimator

Asymptotic normality of the estimator

Abstract

Zero-inflated regression models have had wide application recently and have provenuseful in modeling data with many zeros. Zero-inflated Binomial (ZIB) regression model is an extension of the ordinary binomial distribution that takes into account the excess of zeros. In comparing the probit model to the logistic model, many authors believe that there is little theoretical justification in choosing one formulation over the other in most circumstances involving binary responses. The logit model is considered to be computationally simpler but it is based on a more restrictive assumption of error independence, although many other generalizations have dealt with that assumption as well. By contrast, the probit model assumes that random errors have a multivariate normal distribution. This assumption makes the probit model attractive because the normal distribution provides a good approximation to many other distributions. In this paper, we develop a maximum likelihood estimation procedure for the parameters of a zero-inflated Binomial regression model with probit link function for both component of the model. We establish the existency, consistency and asymptotic normality of the proposed estimator.