# Heterogeneous Overdispersed Count Data Regressions via Double Penalized Estimations

arXiv: https://arxiv.org/abs/2110.03552 · HTML: https://mlsanity.com/paper/2110.03552/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 41 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 7 of 7)

- [Concentration Inequalities for Statistical Inference](https://mlsanity.com/paper/2011.02258/) (2020)
- [Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signals Detection](https://mlsanity.com/paper/1712.03412/) (2017)
- [Model selection and minimax estimation in generalized linear models](https://mlsanity.com/paper/1409.8491/) (2014)
- [Weighted Lasso Estimates for Sparse Logistic Regression: Non-asymptotic Properties with Measurement Error](https://mlsanity.com/paper/2006.06136/) (2020)
- [Directional FDR Control for Sub-Gaussian Sparse GLMs](https://mlsanity.com/paper/2105.00393/) (2021)
- [Fast Bayesian Variable Selection in Binomial and Negative Binomial Regression](https://mlsanity.com/paper/2106.14981/) (2021)
- [A sparse negative binomial mixture model for clustering RNA-seq count data](https://mlsanity.com/paper/1912.02399/) (2019)

## Built on by (most cited first, 1 of 1)

- [High-dimensional prediction for count response via sparse exponential weights](https://mlsanity.com/paper/2410.15381/) (2024)

## Abstract (arXiv)

This paper studies the non-asymptotic merits of the double ℓ1-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.