Robust Scatter Matrix Estimation for High Dimensional Distributions with Heavy Tail

Junwei Lu*, Fang Han, Han Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper studies large scatter matrix estimation for heavy tailed distributions. The contributions of this paper are twofold. First, we propose and advocate to use a new distribution family, the pair-elliptical, for modeling the high dimensional data. The pair-elliptical is more flexible and easier to check the goodness of fit compared to the elliptical. Secondly, built on the pair-elliptical family, we advocate using quantile-based statistics for estimating the scatter matrix. For this, we provide a family of quantile-based statistics. They outperform the existing ones for better balancing the efficiency and robustness. In particular, we show that the propose estimators have comparable performance to the moment-based counterparts under the Gaussian assumption. The method is also tuning-free compared to Catoni's M-estimator for covariance matrix estimation. We further apply the method to conduct a variety of statistical methods. The corresponding theoretical properties as well as numerical performances are provided.

Original languageEnglish (US)
Article number9452112
Pages (from-to)5283-5304
Number of pages22
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2021


  • Heavy-Tailed distribution
  • pair-elliptical distribution
  • quantile-based statistics
  • scatter matrix

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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