Heterogeneous Overdispersed Count Data Regressions via Double Penalized Estimations
This work addresses a specific statistical modeling challenge for count data analysis, representing an incremental theoretical advancement.
The paper tackles the problem of estimating heterogeneous overdispersed count data using negative binomial regressions with double ℓ₁-regularization, proving oracle inequalities for Lasso estimators and demonstrating effectiveness through simulations and real data analysis.
This paper studies the non-asymptotic merits of the double $\ell_1$-regularized for heterogeneous overdispersed count data via negative binomial regressions. Under the restricted eigenvalue conditions, we prove the oracle inequalities for Lasso estimators of two partial regression coefficients for the first time, using concentration inequalities of empirical processes. Furthermore, derived from the oracle inequalities, the consistency and convergence rate for the estimators are the theoretical guarantees for further statistical inference. Finally, both simulations and a real data analysis demonstrate that the new methods are effective.