18
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Quasi shrinkage estimation of a block-structured covariance matrix

ORCID Icon, ORCID Icon & ORCID Icon
Received 08 Nov 2022, Accepted 03 Jun 2024, Published online: 03 Jul 2024

References

  • Cui X, Lin C, Zhao J, et al. Covariance structure regularization via Frobenius norm discrepancy. Linear Algebra Appl. 2016;510:124–145. doi: 10.1016/j.laa.2016.08.013
  • Lin L, Higham NJ, Pan J. Covariance structure regularization via entropy loss function. Comput Statist Data Anal. 2014;72:315–327. doi: 10.1016/j.csda.2013.10.004
  • Filipiak K, Markiewicz A, Mieldzioc A, et al. On projection of a positive definite matrix on a cone of nonnegative definite Toeplitz matrices. Electronic J Linear Algebra. 2018;33:74–82. doi: 10.13001/1081-3810.3750
  • John M, Mieldzioc A. The comparison of the estimators of banded Toeplitz covariance structure under the high-dimensional multivariate model. Comm Statist Simulation Comput. 2020;49(3):734–752. doi: 10.1080/03610918.2019.1614622
  • Lu N, Zimmerman DL. The likelihood ratio test for a separable covariance matrix. Stat Probab Lett. 2005;73(4):449–457. doi: 10.1016/j.spl.2005.04.020
  • Srivastava M, von Rosen T, von Rosen D. Models with a Kronecker product covariance structure: estimation and testing. Math Methods Statist. 2008;17(4):357–370. doi: 10.3103/S1066530708040066
  • Filipiak K, Klein D. Approximation with a Kronecker product structure with one component as compound symmetry or autoregression. Electronic J Linear Algebra. 2018;559:11–33. doi: 10.1016/j.laa.2018.08.031
  • Filipiak K, Klein D, Mokrzycka M. Estimators comparison of separable covariance structure with one component as compound symmetry matrix. Electronic J Linear Algebra. 2018;33:83–98. doi: 10.13001/1081-3810.3740
  • Filipiak K, Klein D, Markiewicz A, et al. Approximation with a Kronecker product structure with one component as compound symmetry or autoregression via entropy loss function. Linear Algebra Appl. 2021;610:625–646. doi: 10.1016/j.laa.2020.10.013
  • Szatrowski TH. Estimation and testing for block compound symmetry and other patterned covariance matrices with linear and non-linear structure. Technical report No. 107, Dept. of Statistics, Stanford University; 1976.
  • Szatrowski TH. Testing and estimation in the block compound symmetry problem. J Educ Stat. 1982;7(1):3–18. doi: 10.3102/10769986007001003
  • Filipiak K, Klein D. Estimation and testing the covariance structure of doubly multivariate data. In: Filipiak K, Markiewicz A. von Rosen D. editors. Multivariate, Multilinear and Mixed Linear Models, Springer; 2021. p. 131–156.
  • Szczepańska-Álvarez A, Hao C, Liang Y, et al. Estimation equations for multivariate linear models with Kronecker structured covariance matrices. Commun Stat Theory Methods. 2017;46(16):7902–7915. doi: 10.1080/03610926.2016.1165852
  • Janiszewska M, Markiewicz A, Mokrzycka M. Block matrix approximation via entropy loss function. Appl Math (Prague). 2020;65(6):829–844. doi: 10.21136/AM
  • Ohlson M, Von Rosen D. Explicit estimators of parameters in the growth curve model with linearly structured covariance matrices. J Multivar Anal. 2010;101(5):1284–1295. doi: 10.1016/j.jmva.2009.12.023
  • Jensen ST. Covariance hypotheses which are linear in both the covariance and the inverse covariance. Ann Stat. 1988;16(1):302–322. doi: 10.1214/aos/1176350707
  • Anderson TW. Asymptotically efficient estimation of covariance matrices with linear structure. Ann Stat. 1973;1(1):135–141. doi: 10.1214/aos/1193342389
  • Mieldzioc A, Mokrzycka M, Sawikowska A. Identification of block-structured covariance matrix on an example of metabolomic data. Separations. 2021;8(11):205–752. doi: 10.3390/separations8110205
  • Zhang F. The schur complement and its applications. New York: Springer; 2005.
  • Kollo T, Von Rosen D. Advanced multivariate statistics with matrices. Dordrecht: Springer; 2005.
  • Härdle WK, Simar L. Applied multivariate statistical analysis. 4th ed. Switzerland: Springer; 2015.
  • Filipiak K, John M, Markiewiecz A. Comments on Maximum Likelihood Estimation and Projections Under Multivariate Statistical Models. In: Holgersson T, Singull M editors. Recent Developments in Multivariate and Random Matrix Analysis, Springer; 2020. p. 51–66.
  • Fuglede B, Jensen ST. Positive projections of symmetric matrices and Jordan algebras. Expo Math. 2013;31(3):295–303. doi: 10.1016/j.exmath.2013.01.005
  • Magnus J, Neudecker H. Symmetry, 0-1 matrices and Jacobians, a review. Econom Theory. 1986;2(2):157–190. doi: 10.1017/S0266466600011476
  • Magnus J, Neudecker H. Matrix differential calculus with applications in statistics and econometrics. revised edition. Chichester: Wiley; 1999.
  • Fackler PL. Notes on matrix calculus. 2005. Available from: http://www4.ncsu.edu/∼pfackler/MatCalc.pdf.
  • Ledoit O, Wolf M. A well-conditioned estimator for large-dimensional covariance matrices. J Multivar Anal. 2004;88(2):365–411. doi: 10.1016/S0047-259X(03)00096-4
  • Seely J. Quadratic subspaces and completeness. Ann Stat. 1971;42(2):710–721. doi: 10.1214/aoms/1177693420
  • Bodnar T, Gupta AK, Parolya N. Direct shrinkage estimation of large dimensional precision matrix. J Multivar Anal. 2016;146:223–236. doi: 10.1016/j.jmva.2015.09.010
  • Ledoit O, Wolf M. Shrinkage estimation of large covariance matrices: keep it simple, statistician? Working Paper No. 327; 2021.
  • Bodnar O, Bodnar T, Parolya N. Recent advances in shrinkage-based high-dimensional inference. J Multivariate Anal. 2022;188:104826. doi: 10.1016/j.jmva.2021.104826
  • Hannart A, Naveau P. Estimating high dimensional covariance matrices: a new look at the Gaussian conjugate framework. J Multivar Anal. 2014;131:149–162. doi: 10.1016/j.jmva.2014.06.001
  • Ikeda Y, Kubokawa T, Srivastava MS. Comparison of linear shrinkage estimators of a large covariance matrix in normal and non-normal distributions. Comput Stat Data Anal. 2016;95:95–108. doi: 10.1016/j.csda.2015.09.011
  • Zehna WP. Invariance of maximum likelihood estimators. Ann Math Statist. 1966;37(3):744–744. doi: 10.1214/aoms/1177699475
  • Marshall AW, Olkin I, Arnold BC. Inequalities: theory of majorization and its applications. 2nd ed. New York: Springer; 2011. 784.
  • Holgersson T, Pielaszkiewicz J. A collection of moments of the Wishart distribution. In: Holgersson T, Singull M, editors. Recent developments in multivariate and random matrix analysis. Springer; 2020. p. 147–162.
  • Pielaszkiewicz J, Von Rosen D. Multivariate moments in multivariate analysis. In: Filipiak K, Markiewicz A, von Rosen D. editors. Multivariate, multilinear and mixed linear models, Springer; 2021. p. 41–92.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.