Heterogeneous Overdispersed Count Data Regressions via Double Penalized Estimations

TL;DR

This paper introduces a novel double L1-regularized method for modeling heterogeneous overdispersed count data with negative binomial regressions, providing theoretical guarantees and demonstrating effectiveness through simulations and real data analysis.

Contribution

It establishes the first oracle inequalities for Lasso estimators in this context, offering new theoretical insights and practical tools for overdispersed count data analysis.

Findings

Proves oracle inequalities for Lasso estimators under restricted eigenvalue conditions.

Provides consistency and convergence rates for the estimators.

Demonstrates effectiveness through simulations and real data applications.

Abstract

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.