IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v96y2015icp333-340.html
   My bibliography  Save this article

A note on the limiting spectral distribution of a symmetrized auto-cross covariance matrix

Author

Listed:
  • Bai, Zhidong
  • Wang, Chen

Abstract

In Jin et al. (2014), the limiting spectral distribution (LSD) of a symmetrized auto-cross covariance matrix is derived using matrix manipulation. The goal of this note is to provide a new method to derive the LSD, which greatly simplifies the derivation in Jin et al. (2014). Moreover, as a by-product, the moment condition of the underlying random variables can be weakened from 2+δ to 2.

Suggested Citation

  • Bai, Zhidong & Wang, Chen, 2015. "A note on the limiting spectral distribution of a symmetrized auto-cross covariance matrix," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 333-340.
  • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:333-340
    DOI: 10.1016/j.spl.2014.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214003514
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2014.10.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dozier, R. Brent & Silverstein, Jack W., 2007. "Analysis of the limiting spectral distribution of large dimensional information-plus-noise type matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1099-1122, July.
    2. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    3. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    4. Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
    5. Dozier, R. Brent & Silverstein, Jack W., 2007. "On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 678-694, April.
    6. Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Heiny, Johannes & Mikosch, Thomas, 2021. "Large sample autocovariance matrices of linear processes with heavy tails," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 344-375.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Yuling & Zhou, Huanchao & Hu, Jiang, 2023. "The eigenvector LSD of information plus noise matrices and its application to linear regression model," Statistics & Probability Letters, Elsevier, vol. 197(C).
    2. Huanchao Zhou & Zhidong Bai & Jiang Hu, 2023. "The Limiting Spectral Distribution of Large-Dimensional General Information-Plus-Noise-Type Matrices," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1203-1226, June.
    3. Paul, Debashis & Silverstein, Jack W., 2009. "No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 37-57, January.
    4. M. Capitaine, 2013. "Additive/Multiplicative Free Subordination Property and Limiting Eigenvectors of Spiked Additive Deformations of Wigner Matrices and Spiked Sample Covariance Matrices," Journal of Theoretical Probability, Springer, vol. 26(3), pages 595-648, September.
    5. Couillet, Romain, 2015. "Robust spiked random matrices and a robust G-MUSIC estimator," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 139-161.
    6. Couillet, Romain & Pascal, Frédéric & Silverstein, Jack W., 2015. "The random matrix regime of Maronna’s M-estimator with elliptically distributed samples," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 56-78.
    7. Jean-Philippe Bouchaud & Laurent Laloux & M. Augusta Miceli & Marc Potters, 2005. "Large dimension forecasting models and random singular value spectra," Science & Finance (CFM) working paper archive 500066, Science & Finance, Capital Fund Management.
    8. Benaych-Georges, Florent & Nadakuditi, Raj Rao, 2012. "The singular values and vectors of low rank perturbations of large rectangular random matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 120-135.
    9. Bodnar, Taras & Gupta, Arjun K. & Parolya, Nestor, 2014. "On the strong convergence of the optimal linear shrinkage estimator for large dimensional covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 215-228.
    10. Weiming Li & Jianfeng Yao, 2015. "On generalized expectation-based estimation of a population spectral distribution from high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 359-373, April.
    11. Mo, M.Y., 2010. "Universality in complex Wishart ensembles for general covariance matrices with 2 distinct eigenvalues," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1203-1225, May.
    12. Merlevède, F. & Peligrad, M., 2016. "On the empirical spectral distribution for matrices with long memory and independent rows," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2734-2760.
    13. Xie, Junshan & Zeng, Yicheng & Zhu, Lixing, 2021. "Limiting laws for extreme eigenvalues of large-dimensional spiked Fisher matrices with a divergent number of spikes," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    14. Wen, Jun, 2018. "Estimation of two high-dimensional covariance matrices and the spectrum of their ratio," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 1-29.
    15. Wang, Lili & Paul, Debashis, 2014. "Limiting spectral distribution of renormalized separable sample covariance matrices when p/n→0," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 25-52.
    16. Li, Hua & Bai, Zhi Dong & Wong, Wing Keung, 2015. "High dimensional Global Minimum Variance Portfolio," MPRA Paper 66284, University Library of Munich, Germany.
    17. Bo Zhang & Jiti Gao & Guangming Pan & Yanrong Yang, 2023. "Eigen-Analysis for High-Dimensional Time Series Clustering," Monash Econometrics and Business Statistics Working Papers 22/23, Monash University, Department of Econometrics and Business Statistics.
    18. Olivier Ledoit & Michael Wolf, 2017. "Analytical nonlinear shrinkage of large-dimensional covariance matrices," ECON - Working Papers 264, Department of Economics - University of Zurich, revised Nov 2018.
    19. Peña, Daniel & Smucler, Ezequiel & Yohai, Victor J., 2021. "Sparse estimation of dynamic principal components for forecasting high-dimensional time series," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1498-1508.
    20. Tingting Zou & Shurong Zheng & Zhidong Bai & Jianfeng Yao & Hongtu Zhu, 2022. "CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data," Statistical Papers, Springer, vol. 63(2), pages 605-664, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:333-340. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.