IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v96y2005i1p136-171.html
   My bibliography  Save this article

Second-order accurate inference on eigenvalues of covariance and correlation matrices

Author

Listed:
  • Boik, Robert J.

Abstract

Edgeworth expansions and saddlepoint approximations for the distributions of estimators of certain eigenfunctions of covariance and correlation matrices are developed. These expansions depend on second-, third-, and fourth-order moments of the sample covariance matrix. Expressions for and estimators of these moments are obtained. The expansions and moment expressions are used to construct second-order accurate confidence intervals for the eigenfunctions. The expansions are illustrated and the results of a small simulation study that evaluates the finite-sample performance of the confidence intervals are reported.

Suggested Citation

  • Boik, Robert J., 2005. "Second-order accurate inference on eigenvalues of covariance and correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 136-171, September.
    • Handle: RePEc:eee:jmvana:v:96:y:2005:i:1:p:136-171
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(04)00179-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Wang, Suojin, 1992. "General saddlepoint approximations in the bootstrap," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 61-66, January.
    2. Bahjat F. Qaqish, 2003. "A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations," Biometrika, Biometrika Trust, vol. 90(2), pages 455-463, June.
    3. Fujikoshi, Y., 1978. "Asymptotic expansions for the distributions of some functions of the latent roots of matrices in three situations," Journal of Multivariate Analysis, Elsevier, vol. 8(1), pages 63-72, March.
    4. Booth, J. G. & Hall, P. & Wood, A. T. A., 1994. "On the Validity of Edgeworth and Saddlepoint Approximations," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 121-138, October.
    5. Sadanori Konishi, 1977. "Asymptotic expansion for the distribution of a function of latent roots of the covariance matrix," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 389-396, December.
    6. Robert J. Boik, 2003. "Principal component models for correlation matrices," Biometrika, Biometrika Trust, vol. 90(3), pages 679-701, September.
    7. Robert J. Boik, 2002. "Spectral models for covariance matrices," Biometrika, Biometrika Trust, vol. 89(1), pages 159-182, March.
    8. Boik, Robert J., 1998. "A Local Parameterization of Orthogonal and Semi-Orthogonal Matrices with Applications," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 244-276, November.
    9. Thomas J. DiCiccio, 2002. "Accurate confidence limits for scalar functions of vector M-estimands," Biometrika, Biometrika Trust, vol. 89(2), pages 437-450, June.
    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. Boik, Robert J., 2013. "Model-based principal components of correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 310-331.
    2. Boik, Robert J., 2008. "An implicit function approach to constrained optimization with applications to asymptotic expansions," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 465-489, March.

    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. Boik, Robert J., 2013. "Model-based principal components of correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 310-331.
    2. Pourahmadi, Mohsen & Daniels, Michael J. & Park, Trevor, 2007. "Simultaneous modelling of the Cholesky decomposition of several covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 568-587, March.
    3. Zongliang Hu & Zhishui Hu & Kai Dong & Tiejun Tong & Yuedong Wang, 2021. "A shrinkage approach to joint estimation of multiple covariance matrices," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 339-374, April.
    4. Robert Boik, 2008. "Newton Algorithms for Analytic Rotation: an Implicit Function Approach," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 231-259, June.
    5. Yamada, Tomoya, 2013. "Asymptotic properties of canonical correlation analysis for one group with additional observations," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 389-401.
    6. Guosheng Yin & Yu Shen, 2005. "Adaptive Design and Estimation in Randomized Clinical Trials with Correlated Observations," Biometrics, The International Biometric Society, vol. 61(2), pages 362-369, June.
    7. Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 15-36, January.
    8. Jorge A. Sefair & Oscar Guaje & Andrés L. Medaglia, 2021. "A column-oriented optimization approach for the generation of correlated random vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 777-808, September.
    9. Josse, J. & Pagès, J. & Husson, F., 2008. "Testing the significance of the RV coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 82-91, September.
    10. Y. Fong & J. Wakefield & S. De Rosa & N. Frahm, 2012. "A Robust Bayesian Random Effects Model for Nonlinear Calibration Problems," Biometrics, The International Biometric Society, vol. 68(4), pages 1103-1112, December.
    11. Haruhiko Ogasawara, 2009. "Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 995-1017, December.
    12. Peter D. Hoff, 2009. "A hierarchical eigenmodel for pooled covariance estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 971-992, November.
    13. Tsung-Shan Tsou & Wan-Chen Chen, 2013. "Estimation of intra-cluster correlation coefficient via the failure of Bartlett’s second identity," Computational Statistics, Springer, vol. 28(4), pages 1681-1698, August.
    14. Sergei Leonov & Bahjat Qaqish, 2020. "Correlated endpoints: simulation, modeling, and extreme correlations," Statistical Papers, Springer, vol. 61(2), pages 741-766, April.
    15. A. Elijio & V. Čekanavičius, 2015. "Compound Poisson approximation to weighted sums of symmetric discrete variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 195-210, February.
    16. Moysiadis, Theodoros & Fokianos, Konstantinos, 2014. "On binary and categorical time series models with feedback," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 209-228.
    17. Berman, Oded & Krass, Dmitry & Menezes, Mozart B.C., 2013. "Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns," Omega, Elsevier, vol. 41(4), pages 766-779.
    18. B. C. Sutradhar, 2008. "On auto-regression type dynamic mixed models for binary panel data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 209-221.
    19. Farrell, Patrick J. & Sutradhar, Brajendra C., 2006. "A non-linear conditional probability model for generating correlated binary data," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 353-361, February.
    20. Luca Bagnato & Antonio Punzo, 2021. "Unconstrained representation of orthogonal matrices with application to common principal components," Computational Statistics, Springer, vol. 36(2), pages 1177-1195, June.

    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:jmvana:v:96:y:2005:i:1:p:136-171. 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.