Title: Semi-Parametric Models for Negative Binomial Panel Data

Author(s): Brajendra C. Sutradhar, Vandna Jowaheer and R. Prabhakar Rao
Issue: Volume 78 Series A Part 2 Year 2016
Pages: 269 -- 303
This paper considers a semi-parametric model for longitudinal negative binomial counts under the assumption that the repeated count responses follow an ARMA type non-stationary correlation structure. A step-by-step estimation approach is developed which provides consistent estimators for the non-parametric function, the auto-correlation structure and overdispersion parameter involved in the marginal negative binomial model, subsequently yielding a consistent estimator for the main regression parameter. Proofs for the consistency properties of the estimators are given. Also the convergence rates for the estimators of the non-parametric function as well as main parameters of the model are derived.
AMS (2000) subject classification. Primary 62F10, 62H20; Secondary 62F12, 62H12.
Keywords and phrases: Auto-correlations for negative binomial counts, Kernel based semi-parametric generalized quasi-likelihood estimation, Moments for correlation estimation, Non-parametric function, Quasi-likelihood estimation, Semi-parametric marginal regression model.