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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 power law of the distributions of credits (e.g., the number of "likes") of viral posts in social media, we introduce the high-dimensional tail index regression and methods of estimation and inference for its parameters. We propose a regularized estimator, establish its consistency, and derive its convergence rate. To conduct inference, we propose to debias the regularized estimate, and establish the asymptotic normality of the debiased estimator. Simulation studies support our theory. These methods are applied to text analyses of viral posts in X (formerly Twitter) concerning LGBTQ+.

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  • 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.
    • Handle: RePEc:arx:papers:2403.01318
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    File URL: http://arxiv.org/pdf/2403.01318
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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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