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High-Dimensional Tail Index Regression: with An Application to Text Analyses of Viral Posts in Social Media

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  • Yuya Sasaki
  • Jing Tao
  • Yulong Wang

Abstract

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.

Suggested Citation

  • Yuya Sasaki & Jing Tao & Yulong Wang, 2024. "High-Dimensional Tail Index Regression: with An Application to Text Analyses of Viral Posts in Social Media," Papers 2403.01318, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2403.01318
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    References listed on IDEAS

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    1. Nicolau, João & Rodrigues, Paulo M.M. & Stoykov, Marian Z., 2023. "Tail index estimation in the presence of covariates: Stock returns’ tail risk dynamics," Journal of Econometrics, Elsevier, vol. 235(2), pages 2266-2284.
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