Optimal Non-Asymptotic Bounds for the Sparse β Model

Xiaowei Yang, Lu Pan, Kun Cheng and Chao Liu ()
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Xiaowei Yang: College of Mathematics, Sichuan University, Chengdu 610017, China
Lu Pan: Department of Statistics, Central China Normal University, Wuhan 430079, China
Kun Cheng: School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100080, China
Chao Liu: College of Economics, Shenzhen University, Shenzhen 518060, China

Mathematics, 2023, vol. 11, issue 22, 1-19

Abstract: This paper investigates the sparse β model with 𝓁 1 penalty in the field of network data models, which is a hot topic in both statistical and social network research. We present a refined algorithm designed for parameter estimation in the proposed model. Its effectiveness is highlighted through its alignment with the proximal gradient descent method, stemming from the convexity of the loss function. We study the estimation consistency and establish an optimal bound for the proposed estimator. Empirical validations facilitated through meticulously designed simulation studies corroborate the efficacy of our methodology. These assessments highlight the prospective contributions of our methodology to the advanced field of network data analysis.

Keywords: sparse ? model; ? 1 penalty; proximal gradient decent; consistency analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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