Square‐Root LASSO for High‐Dimensional Sparse Linear Systems with Weakly Dependent Errors |
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| Authors: | Fang Xie Zhijie Xiao |
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| Affiliation: | 1. Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, China;2. UM Zhuhai Research Institute, Zhuhai, China;3. Department of Economics, Boston College, Chestnut Hill, MA, USA;4. Center for Economic Research, Shandong University, Jinan, China |
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| Abstract: | We study the square‐root LASSO method for high‐dimensional sparse linear models with weakly dependent errors. The asymptotic and non‐asymptotic bounds for the estimation errors are derived. Our results cover a wide range of weakly dependent errors, including α‐mixing, ρ‐mixing, ?‐mixing, and m‐dependent types. Numerical simulations are conducted to show the consistency property of square‐root LASSO. An empirical application to financial data highlights the importance of the results and method. |
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| Keywords: | high‐dimensional linear model square‐root LASSO
α ‐mixing
ρ ‐mixing
ϕ ‐mixing
m‐dependent estimation consistency |
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