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Keywords:
approximation; block covariance structure; entropy loss function
approximation; block covariance structure; entropy loss function
Summary:
The aim of the paper is to present a procedure for the approximation of a symmetric positive definite matrix by symmetric block partitioned matrices with structured off-diagonal blocks. The entropy loss function is chosen as approximation criterion. This procedure is applied in a simulation study of the statistical problem of covariance structure identification.
References:
[1] Cui, X., Li, C., Zhao, J., Zeng, L., Zhang, D., Pan, J.: Covariance structure regularization via Frobenius-norm discrepancy. Linear Algebra Appl. 510 (2016), 124-145. DOI 10.1016/j.laa.2016.08.013 | MR 3551623 | Zbl 1352.62090
[2] Dey, D. K., Srinivasan, C.: Estimation of a covariance matrix under Stein's loss. Ann. Stat. 13 (1985), 1581-1591. DOI 10.1214/aos/1176349756 | MR 0811511 | Zbl 0582.62042
[3] Fackler, P. L.: Notes on matrix calculus. Available at https://studyres.com/doc/15927579/notes-on-matrix-calculus (2005), 14 pages.
[4] Filipiak, K., Klein, D.: Approximation with a Kronecker product structure with one component as compound symmetry or autoregression. Linear Algebra Appl. 559 (2018), 11-33. DOI 10.1016/j.laa.2018.08.031 | MR 3857535 | Zbl 1402.62117
[5] Filipiak, K., Klein, D., Markiewicz, A., Mokrzycka, M.: Approximation with a Kronecker product structure with one component as compound symmetry or autoregression via entropy loss function. (to appear) in Linear Algebra Appl. (2020). DOI 10.1016/j.laa.2020.10.013 | MR 3857535
[6] Filipiak, K., Klein, D., Mokrzycka, M.: Estimators comparison of separable covariance structure with one component as compound symmetry matrix. Electron. J. Linear Algebra 33 (2018), 83-98. DOI 10.13001/1081-3810.3740 | MR 3962256 | Zbl 1406.15020
[7] Filipiak, K., Markiewicz, A., Mieldzioc, A., Sawikowska, A.: On projection of a positive definite matrix on a cone of nonnegative definite Toeplitz matrices. Electron. J. Linear Algebra 33 (2018), 74-82. DOI 10.13001/1081-3810.3750 | MR 3962255 | Zbl 1406.15028
[8] Gilson, M., Dahmen, D., Moreno-Bote, R., Insabato, A., Helias, M.: The covariance perceptron: A new paradigm for classication and processing of time series in recurrent neuronal networks. Available at https://www.biorxiv.org/content/10.1101/562546v4 (2020), 39 pages. DOI 10.1101/562546
[9] James, W., Stein, C.: Estimation with quadratic loss. Proc. 4th Berkeley Symp. Math. Stat. Probab. Vol. 1 University of California Press, Berkeley (1961), 361-379. MR 0133191 | Zbl 1281.62026
[10] John, M., Mieldzioc, A.: The comparison of the estimators of banded Toeplitz covariance structure under the high-dimensional multivariate model. Commun. Stat., Simulation Comput. 49 (2020), 734-752. DOI 10.1080/03610918.2019.1614622 | MR 4068485
[11] Kollo, T., Rosen, D. von: Advanced Multivariate Statistics with Matrices. Mathematics and Its Applications 579. Springer, Dordrecht (2005). DOI 10.1007/1-4020-3419-9 | MR 2162145 | Zbl 1079.62059
[12] Lin, L., Higham, N. J., Pan, J.: Covariance structure regularization via entropy loss function. Comput. Stat. Data Anal. 72 (2014), 315-327. DOI 10.1016/j.csda.2013.10.004 | MR 3139365 | Zbl 06983908
[13] Lu, N., Zimmerman, D. L.: The likelihood ratio test for a separable covariance matrix. Stat. Probab. Lett. 73 (2005), 449-457. DOI 10.1016/j.spl.2005.04.020 | MR 2187860 | Zbl 1071.62052
[14] Magnus, J. R., Neudecker, H.: Symmetry, 0-1 matrices and Jacobians: A review. Econom. Theory 2 (1986), 157-190. DOI 10.1017/S0266466600011476
[15] Magnus, J. R., Neudecker, H.: Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley Series in Probability and Statistics. Wiley, Chichester (1999). DOI 10.1002/9781119541219 | MR 1698873 | Zbl 0912.15003
[16] Mieldzioc, A., Mokrzycka, M., Sawikowska, A.: Covariance regularization for metabolomic data on the drought resistance of barley. Biometrical Lett. 56 (2019), 165-181. DOI 10.2478/bile-2019-0010
[17] Pan, J.-X., Fang, K.-T.: Growth Curve Models and Statistical Diagnostics. Springer Series in Statistics. Springer, New York (2002). DOI 10.1007/978-0-387-21812-0 | MR 1937691 | Zbl 1024.62025
[18] Srivastava, M. S., Rosen, T. von, Rosen, D. von: Models with a Kronecker product covariance structure: Estimation and testing. Math. Methods Stat. 17 (2008), 357-370. DOI 10.3103/S1066530708040066 | MR 2483463 | Zbl 1231.62101
[19] Szatrowski, T. H.: Estimation and testing for block compound symmetry and other patterned covariance matrices with linear and non-linear structure. Technical Report OLK NSF 107, Stanford University, Stanford (1976), 187 pages. MR 2626007
[20] Szatrowski, T. H.: Testing and estimation in the block compound symmetry problem. J. Educ. Behavioral Stat. 7 (1982), 3-18. DOI 10.3102/10769986007001003
[21] Szczepańska-Álvarez, A., Hao, C., Liang, Y., Rosen, D. von: Estimation equations for multivariate linear models with Kronecker structured covariance matrices. Commun. Stat., Theory Methods 46 (2017), 7902-7915. DOI 10.1080/03610926.2016.1165852 | MR 3660028 | Zbl 1373.62262
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