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Nonparametric estimation of large covariance matrices with conditional sparsity

Author

Listed:
  • Wang, Hanchao
  • Peng, Bin
  • Li, Degui
  • Leng, Chenlei

Abstract

This paper studies estimation of covariance matrices with conditional sparse structure. We overcome the challenge of estimating dense matrices using a factor structure, the challenge of estimating large-dimensional matrices by postulating sparsity on covariance of random noises, and the challenge of estimating varying matrices by allowing factor loadings to smoothly change. A kernel-weighted estimation approach combined with generalised shrinkage is proposed. Under some technical conditions, we derive uniform consistency for the developed estimation method and obtain convergence rates. Numerical studies including simulation and an empirical application are presented to examine the finite-sample performance of the developed methodology.

Suggested Citation

  • Wang, Hanchao & Peng, Bin & Li, Degui & Leng, Chenlei, 2021. "Nonparametric estimation of large covariance matrices with conditional sparsity," Journal of Econometrics, Elsevier, vol. 223(1), pages 53-72.
    • Handle: RePEc:eee:econom:v:223:y:2021:i:1:p:53-72
    DOI: 10.1016/j.jeconom.2020.09.002
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    Cited by:

    1. Jin Yuan & Xianghui Yuan, 2023. "A Best Linear Empirical Bayes Method for High-Dimensional Covariance Matrix Estimation," SAGE Open, , vol. 13(2), pages 21582440231, June.

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    More about this item

    Keywords

    Approximate factor model; Kernel estimation; Large covariance matrix; Sparsity; Uniform convergence;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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