Yuya Sasaki, Jing Tao, Yulong Wang
arXiv 2 Mar 2024 · Statistics — Machine Learning
arXiv:2403.01318 · PDF · DOI · OpenAlex · Extracted main text
Motivated by the empirical observation of power-law distributions in the credits (e.g., "likes") of viral social media posts, we introduce a high-dimensional tail index regression model and propose methods for estimation and inference of its parameters. First, we present a regularized estimator, establish its consistency, and derive its convergence rate. Second, we introduce a debiasing technique for the regularized estimator to facilitate inference and prove its asymptotic normality. Third, we extend our approach to handle large-scale online streaming data using stochastic gradient descent. Simulation studies corroborate our theoretical findings. We apply these methods to the text analysis of viral posts on X (formerly Twitter) related to LGBTQ+ topics.
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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 | Cai, T Tony and Guo, Zijian and Ma, Rong (2023) Statistical inference for high-dimensional generalized linear models with binary outcomes | 0.754 | 7 | 4 | 43% |
| 2 | Sara van de Geer and Peter Bühlmann and Ya’acov Ritov and Ruben Deze… (2014) On asymptotically optimal confidence regions and tests for high-dimensional models | 0.737 | 3 | 3 | 67% |
| 3 | Zhang, Cun-Hui and Zhang, Stephanie S (2014) Confidence intervals for low dimensional parameters in high dimensional linear models | 0.737 | 3 | 3 | 67% |
| 4 | Wang, Hansheng and Tsai, Chih-Ling (2009) Tail index regression | 0.737 | 3 | 2 | 100% |
| 5 | Gardes, L. and Girard, S (2010) Conditional extremes from heavy-tailed distributions: An application to the estimation of extreme rain fall return levels | 0.644 | 2 | 2 | 100% |
| 6 | de Haan, L. and A. Ferreira (2007) Extreme Value Theory: An Introduction | 0.644 | 2 | 2 | 100% |
| 7 | Gabaix, Xavier (2009) Power Laws in Economics and Finance | 0.644 | 2 | 2 | 100% |
| 8 | Gabaix, Xavier (2016) Power Laws in Economics: An Introduction | 0.644 | 2 | 2 | 100% |
| 9 | Negahban, Sahand and Yu, Bin and Wainwright, Martin J and Ravikumar,… (2009) A unified framework for high-dimensional analysis of $ m $-estimators with decomposable regularizers | 0.644 | 2 | 2 | 100% |
| 10 | van de Geer, Sara A (2008) High-dimensional generalized linear models and the lasso | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 40 scored citations.