Asymptotically independent U-statistics in high-dimensional testing

@article{He2018AsymptoticallyIU,
  title={Asymptotically independent U-statistics in high-dimensional testing},
  author={Yinqiu He and Gongjun Xu and Chong Wu and Wei Pan},
  journal={arXiv: Statistics Theory},
  year={2018}
}
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper constructs a family of U-statistics as unbiased estimators of the $\ell_p$-norms of those features. We show that under the null hypothesis, the U-statistics of different finite orders are asymptotically independent and normally distributed. Moreover, they are also… 
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