ELASTIC-NET REGULARIZED HIGH-DIMENSIONAL NEGATIVE BINOMIAL REGRESSION: CONSISTENCY AND WEAK SIGNAL DETECTION
ELASTIC-NET REGULARIZED HIGH-DIMENSIONAL NEGATIVE BINOMIAL REGRESSION: CONSISTENCY AND WEAK SIGNAL DETECTION
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DOI：
10.5705/ss.202019.0315
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发表时间：
2022-01-01
影响因子：
1.4
通讯作者：
Jia, Jinzhu
中科院分区：
文献类型：
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作者：
Zhang, Huiming;Jia, Jinzhu
我们研究了计数数据的稀疏负二项回归(NBR)，证明了使用弹性网估计的非渐近优势。利用相容因子条件和Stabil条件，给出了NBR弹性网估计的两种预言式。第二类先知不等式是随机设计的，可以推广到许多L(1)+L(2)正则M-估计，相应的经验过程具有随机Lipschitz性质。对于某些大概率事件，我们给出了负二项变量加权和的上界经验过程的浓度不等式。如果真稀疏向量中的非零分量大于最弱信号检测阈值的适当选择，我们通过证明符号一致性来应用该方法。在第二个应用中，我们高概率地证明了分组效应不等式。第三，在对设计矩阵的某些假设下，如果最弱的信号检测阈值大于转向参数到一个已知常数，我们可以以很高的概率恢复真实变量集。最后，我们简要地讨论了无偏弹性网估计量，并给出了数值研究。
We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the Compatibility Factor Condition and the Stabil Condition. The second type of oracle inequality is for the random design and can be extended to many l(1) + l(2) regularized M-estimations, with the corresponding empirical process having stochastic Lipschitz properties. We derive the concentration inequality for the suprema empirical processes for the weighted sum of negative binomial variables to show some high-probability events. We apply the method by showing the sign consistency, provided that the nonzero components in the true sparse vector are larger than a proper choice of the weakest signal detection threshold. In the second application, we show the grouping effect inequality with high probability. Third, under some assumptions for a design matrix, we can recover the true variable set with a high probability if the weakest signal detection threshold is large than the turning parameter up to a known constant. Lastly, we briefly discuss the de-biased elastic-net estimator, and numerical studies are given to support the proposal.