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High-Dimensional Linear Models: A Random Matrix Perspective

Author

Listed:
  • Jamshid Namdari

    (University of California)

  • Debashis Paul

    (University of California)

  • Lili Wang

    (Zhejiang Gongshang University)

Abstract

Professor C.R.Rao’s Linear Statistical Inference is a classic that has motivated several generations of statisticians in their pursuit of theoretical research. This paper looks into some of the fundamental problems associated with linear models, but in a scenario where the dimensionality of the observations is comparable to the sample size. This perspective, largely driven by contemporary advancements in random matrix theory, brings new insights and results that can be helpful even for solving relatively low-dimensional problems. This overview also brings into focus the fundamental roles played by the eigenvalues of large covariance-type matrices in the theory of high-dimensional multivariate statistics.

Suggested Citation

  • Jamshid Namdari & Debashis Paul & Lili Wang, 2021. "High-Dimensional Linear Models: A Random Matrix Perspective," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 645-695, August.
    • Handle: RePEc:spr:sankha:v:83:y:2021:i:2:d:10.1007_s13171-020-00219-y
    DOI: 10.1007/s13171-020-00219-y
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    References listed on IDEAS

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