High-Dimensional Tail Index Regression: with An Application to Text
  Analyses of Viral Posts in Social Media
Yuya Sasaki Jing Tao Yulong Wang
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+.