Embracing the blessing of dimensionality in factor models

Quefeng Li Guang Cheng Jianqing Fan Yuyan Wang

Statistics Theory and Methods mathscidoc:1912.43392

Journal of the American Statistical Association, 113, (521), 380-389, 2018.1
Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the blessing of dimensionality has not yet been fully embraced in the literature: much of the available data are often ignored in constructing covariance matrix estimates. If our goal is to accurately estimate a covariance matrix of a set of targeted variables, shall we employ additional data, which are beyond the variables of interest, in the estimation? In this article, we provide sufficient conditions for an affirmative answer, and further quantify its gain in terms of Fisher information and convergence rate. In fact, even an oracle-like result (as if all the factors were known) can be achieved when a sufficiently large number of variables is used. The idea of using data as much as possible
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  title={Embracing the blessing of dimensionality in factor models},
  author={Quefeng Li, Guang Cheng, Jianqing Fan, and Yuyan Wang},
  booktitle={Journal of the American Statistical Association},
Quefeng Li, Guang Cheng, Jianqing Fan, and Yuyan Wang. Embracing the blessing of dimensionality in factor models. 2018. Vol. 113. In Journal of the American Statistical Association. pp.380-389. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114126798064952.
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