Sparse principal component analysis for high‐dimensional stationary time series
Sparse principal component analysis for high‐dimensional stationary time series
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DOI：
10.1111/sjos.12664
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发表时间：
2021-09
影响因子：
1
通讯作者：
Kou Fujimori;Yuichi Goto;Y. Liu;M. Taniguchi
中科院分区：
文献类型：
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作者：
Kou Fujimori;Yuichi Goto;Y. Liu;M. Taniguchi
本文研究了高维平稳过程的稀疏主成分分析。当过程规模较大时，标准主成分分析的性能较差。我们建立了包括重尾时间序列在内的大类过程的惩罚主成分估计的oracle不等式。给出了估计量的收敛速度。我们还阐明了在惩罚估计器中选择调谐参数的理论速率。通过数值模拟验证了稀疏主成分分析的性能。通过对平均温度数据的分析，说明了稀疏主成分分析在时间序列数据中的应用。
We consider the sparse principal component analysis for high‐dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish oracle inequalities for penalized principal component estimators for the large class of processes including heavy‐tailed time series. The rate of convergence of the estimators is established. We also elucidate the theoretical rate for choosing the tuning parameter in penalized estimators. The performance of the sparse principal component analysis is demonstrated by numerical simulations. The utility of the sparse principal component analysis for time series data is exemplified by the application to average temperature data.