Approaches to High-Dimensional Covariance and Precision Matrix Estimations

Jianqing Fan*, Yuan Liao, Han Liu

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations


This chapter introduces several recent developments for estimating large covariance and precision matrices without assuming the covariance matrix to be sparse. It explains two methods for covariance estimation: namely covariance estimation via factor analysis, and precision Matrix Estimation and Graphical Models. The low rank plus sparse representation holds on the population covariance matrix. The chapter presents several applications of these methods, including graph estimation for gene expression data, and several financial applications. It then shows how estimating covariance matrices of high-dimensional asset excess returns play a central role in applications of portfolio allocations and in risk management. The chapter explains the factor pricing model, which is one of the most fundamental results in finance. It elucidates estimating risks of large portfolios and large panel test of factor pricing models. The chapter illustrates the recent developments of efficient estimations in panel data models.

Original languageEnglish (US)
Title of host publicationFinancial Signal Processing and Machine Learning
Number of pages35
ISBN (Electronic)9781118745540
ISBN (Print)9781118745670
StatePublished - Apr 29 2016


  • Covariance estimation
  • Factor pricing model
  • Financial applications
  • Gene expression
  • Graphical models
  • High-dimensional covariance
  • Panel data models
  • Precision Matrix

ASJC Scopus subject areas

  • General Engineering
  • General Computer Science


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