NECESSARY AND SUFFICIENT CONDITIONS FOR THE ASYMPTOTIC DISTRIBUTIONS OF COHERENCE OF ULTRA-HIGH DIMENSIONAL RANDOM MATRICES

@article{Shao2014NECESSARYAS,
  title={NECESSARY AND SUFFICIENT CONDITIONS FOR THE ASYMPTOTIC DISTRIBUTIONS OF COHERENCE OF ULTRA-HIGH DIMENSIONAL RANDOM MATRICES},
  author={Q. Shao and Wen-Xin Zhou},
  journal={Annals of Probability},
  year={2014},
  volume={42},
  pages={623-648}
}
Let $\mathbf {x}_1,\ldots,\mathbf {x}_n$ be a random sample from a $p$-dimensional population distribution, where $p=p_n\to\infty$ and $\log p=o(n^{\beta})$ for some $0 0$, where $\alpha$ satisfies $\beta=\alpha/(4-\alpha)$. Asymptotic distributions of $L_n$ are also proved under the same sufficient condition. Similar results remain valid for $m$-coherence when the variables of the population are $m$ dependent. The proofs are based on self-normalized moderate deviations, the Stein-Chen method… Expand
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