Shaomin Li, Haoyu Wei, Xiaoyu Lei
arXiv 7 Oct 2021 · Statistics — Methodology · publishedMathematics (2022) · 9 citations (OpenAlex)
arXiv:2110.03552 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Bickel, P. J., Y. Ritov, A. B. Tsybakov, et al (2009) Simultaneous analysis of lasso and dantzig selector | 0.644 | 3 | 2 | 67% |
| 2 | Zhang, H. and J. Jia (2022) Elastic-net regularized high-dimensional negative binomial regression: Consistency and weak signals detection | 0.644 | 3 | 2 | 67% |
| 3 | Wang, Z., S. Ma, M. Zappitelli, C. Parikh, C.-Y. Wang, and P. Devara… (2016) Penalized count data regression with application to hospital stay after pediatric cardiac surgery | 0.644 | 2 | 2 | 100% |
| 4 | Candes, E., T. Tao, et al (2007) The dantzig selector: Statistical estimation when p is much larger than n | 0.511 | 2 | 1 | 100% |
| 5 | Tibshirani, R (1996) Regression shrinkage and selection via the lasso | 0.405 | 1 | 1 | 100% |
| 6 | Hilbe, J. M (2011) Negative binomial regression | 0.405 | 1 | 1 | 100% |
| 7 | Qiu, Y., S. X. Chen, and D. Nettleton (2018) Detecting rare and faint signals via thresholding maximum likelihood estimators | 0.405 | 1 | 1 | 100% |
| 8 | Adamczak, R (2008) A tail inequality for suprema of unbounded empirical processes with applications to markov chains | 0.405 | 1 | 1 | 100% |
| 9 | Cui, C., J. Jia, Y. Xiao, and H. Zhang (2021) Directional fdr control for sub-gaussian sparse glms | 0.405 | 1 | 1 | 100% |
| 10 | Dai, H., Y. Bao, and M. Bao (2013) Maximum likelihood estimate for the dispersion parameter of the negative binomial distribution | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 31 scored citations.