Semiparametric Robust Zero-Altered Models for Regression Analysis of Count Data

Thomas M. Menino Convention & Exhibition Center 

We propose a flexible class of semiparametric regression models for count data based on zero-altered distributions (ZADs), estimated via the generalized method of moments (GMM). Unlike conventional parametric GLMs (e.g., Poisson or negative binomial), our approach accommodates both under- and over-dispersion while retaining full support on the nonnegative integers. By relying only on moment conditions rather than full likelihoods, the GMM framework offers robust inference even under distributional misspecification, and ensures consistent estimation when higher-order features are misspecified. Theoretical results establish consistency and asymptotic normality of the estimators under broad conditions. The robustness and flexibility of the proposed models are extensively demonstrated using three real-world data sets-covering diverse dispersion patterns and practical domains, which highlight superior performance relative to standard GLMs. Accompanying R functions facilitate straightforward implementation for applied researchers.

Generalized method of moments



over-dispersion





under-dispersion


misspecification



excess zeroes

semiparametric methods 

Section on Nonparametric Statistics