Estimation of functionals of sparse covariance matrices

Jianqing Fan Philippe Rigollet Weichen Wang

Statistics Theory and Methods mathscidoc:1912.43379

Annals of statistics, 43, (6), 2706, 2015
High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other r norms. Motivated by the computation of critical values of such tests, we investigate the difficulty of estimation the functionals of sparse correlation matrices. Specifically, we show that simple plug-in procedures based on thresholded estimators of correlation matrices are sparsity-adaptive and minimax optimal over a large class of correlation matrices. Akin to previous results on functional estimation, the minimax rates exhibit an elbow phenomenon. Our results are further illustrated in simulated data as well as an empirical study of data arising in financial econometrics.
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@inproceedings{jianqing2015estimation,
  title={Estimation of functionals of sparse covariance matrices},
  author={Jianqing Fan, Philippe Rigollet, and Weichen Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114042589171939},
  booktitle={Annals of statistics},
  volume={43},
  number={6},
  pages={2706},
  year={2015},
}
Jianqing Fan, Philippe Rigollet, and Weichen Wang. Estimation of functionals of sparse covariance matrices. 2015. Vol. 43. In Annals of statistics. pp.2706. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114042589171939.
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