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Applications on linear spectral statistics of high-dimensional sample covariance matrix with divergent spectrum

Author

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  • Zhang, Yangchun
  • Zhou, Yirui
  • Liu, Xiaowei

Abstract

In large-scale statistical inference when the sample size n and dimension p both tend to infinity, the original central limit theorems (CLTs) produce the bounded spectral norm assumption of the covariance matrix which excludes many important applications. Recently, a new CLT (DCLT) was established for the unbounded population spectrum, allowing utilization with divergent spectral norm population models. Comparative simulations are provided in this study for the original CLT and DCLT, and applications for John's test, interval estimation, and point estimation. Numerical results document the greater performance of DCLT than the original CLT in most cases. Moreover, for the bounded population spectrum, the DCLT modifies the limiting mean and variance shift, and gains preferable theoretical results with small p and n. Real data implementation are illustrated on a radio frequency dataset.

Suggested Citation

  • Zhang, Yangchun & Zhou, Yirui & Liu, Xiaowei, 2023. "Applications on linear spectral statistics of high-dimensional sample covariance matrix with divergent spectrum," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:csdana:v:178:y:2023:i:c:s0167947322001979
    DOI: 10.1016/j.csda.2022.107617
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    References listed on IDEAS

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