Heterogeneous Overdispersed Count Data Regressions via Double-Penalized Estimations

Recently, the high-dimensional negative binomial regression (NBR) for count data has been widely used in many scientific fields. However, most studies assumed dispersion parameter as a constant, which may not be satisfied practice. This paper variable selection and estimation heterogeneous NBR models, model function. Specifically, we proposed double applied ℓ1-penalty to both regressions. Under restricted eigenvalue conditions, prove oracle inequalities lasso estimators of two partial coefficients first time, using concentration empirical processes. Furthermore, derived from inequalities, consistency convergence rate are theoretical guarantees further statistical inference. Finally, simulations real analysis demonstrate that new methods effective.