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.

翻译：本文研究了通过负二进制回归,对多种多散的计算数据实行双倍 ell_1美元常规化的双重值为1美元的非正常值。在受限制的双元值条件下,我们用经验过程的集中性不平等,首次证明两个部分回归系数的拉斯索估计者有甲骨文不平等。此外,由于甲骨文不平等,估计者的一致性和趋同率是进一步统计推论的理论保障。 最后,模拟和真实数据分析都表明新方法是有效的。