Kiểm định khối chéo cho ma trận hiệp phương sai có chiều cao

Al-Shalalfa M, Alhajj R (2007) Attractive feature reduction approach for colon data classification. In: 21st International Conference on Advanced Information Networking and Applications Workshops (AINAW’07), vol 1. IEEE, Niagara Falls, ON, Canada, pp 678–683, https://doi.org/10.1109/AINAW.2007.103 Anderson TW (1984) An introduction to multivariate statistical analysis, 2nd edn. Wiley, New York Bai Z, Jiang D, Yao J et al (2009) Corrections to LRT on large dimensional covariance matrix by RMT. Ann Stat 37(6B):3822–3840. https://doi.org/10.1214/09-AOS694 Bao Z, Hu J, Pan G et al (2017) Test of independence for high-dimensional random vectors based on block correlation matrices. Electron J Stat 11:1527–1548. https://doi.org/10.1214/17-EJS1259 Berisa T, Pickrell JK (2016) Approximately independent linkage disequilibrium blocks in human populations. Bioinformatics 32(2):283–285. https://doi.org/10.1093/bioinformatics/btv546 Bodnar T, Dette H, Parolya N (2019) Testing for independence of large dimensional vectors. Ann Stat 47(5):2977–3008. https://doi.org/10.1214/18-AOS1771 Cai T, Jiang T (2011) Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices. Ann Stat 39(3):1496–1525. https://doi.org/10.1214/11-AOS879 Cai T, Ma Z (2013) Optimal hypothesis testing for high dimensional covariance matrices. Bernoulli 19(5B):2359–2388. https://doi.org/10.3150/12-BEJ455 Chen S, Zhang L, Zhong P (2010) Tests for high-dimensional covariance matrices. J Am Stat Assoc 105(490):810–819. https://doi.org/10.1198/jasa.2010.tm09560 Devijver E, Gallopin M (2018) Block-diagonal covariance selection for high-dimensional gaussian graphical models. J Am Stat Assoc 113(521):306–314. https://doi.org/10.1080/01621459.2016.1247002 Dudoit S, Fridlyand J, Speed TP (2002) Comparison of discrimination methods for the classification of tumors using gene expression data. J Am Stat Assoc 97(457):77–87. https://doi.org/10.1198/016214502753479248 He Y, Xu G, Wu C et al (2021) Asymptotically independent u-statistics in high-dimensional testing. Ann Stat 49(1):154–181. https://doi.org/10.1214/20-AOS1951 Hyodo M, Shutoh N, Nishiyama T et al (2015) Testing block-diagonal covariance structure for high-dimensional data. Stat Neerl 69(4):460–482. https://doi.org/10.1111/stan.12068 Jiang D, Qi Y (2015) Likelihood ratio tests for high-dimensional normal distributions. Scand J Stat 42(4):988–1009. https://doi.org/10.1111/sjos.12147 Jiang D, Jiang T, Yang F (2012) Likelihood ratio tests for covariance matrices of high-dimensional normal distributions. J Stat Plan Inference 142(8):2241–2256. https://doi.org/10.1016/j.jspi.2012.02.057 Jiang D, Bai Z, Zheng S (2013) Testing the independence of sets of large-dimensional variables. Sci China Math 56(1):135–147. https://doi.org/10.1007/s11425-012-4501-0 Jiang T, Yang F (2013) Central limit theorems for classical likelihood ratio tests for high-dimensional normal distributions. Ann Stat 41(4):2029–2074. https://doi.org/10.1214/13-AOS1134 John S (1971) Some optimal multivariates tests. Biometrika 58(1):123–127. https://doi.org/10.1093/biomet/58.1.123 Kan R (2008) From moments of sum to moments of product. J Multivar Anal 99(3):542–554. https://doi.org/10.1016/j.jmva.2007.01.013 Kumar SS, Sumathi A, Ramaraj DE (2012) Development of an efficient clustering technique for colon dataset. Int J Eng Innovative Technol 1(5):83–86 Ledoit O, Wolf M (2002) Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. Ann Stat 30(4):1081–1102. https://doi.org/10.1214/aos/1031689018 Li W, Yao J (2018) On structure testing for component covariance matrices of a high dimensional mixture. J R Stat Soc Ser B (Stat Methodol) 80(2):293–318. https://doi.org/10.1111/rssb.12248 Li W, Chen J, Yao J (2017) Testing the independence of two random vectors where only one dimension is large. Statistics 51(1):141–153. https://doi.org/10.1080/02331888.2016.1266988 Lin Z, Xiang Y (2008) A hypothesis test for independence of sets of variates in high dimensions. Statist Probab Lett 78(17):2939–2946. https://doi.org/10.1016/j.spl.2008.05.003 Marques F, Coelho C, Marques P (2013) The block-matrix sphericity test: exact and near-exact distributions for the test statistic. Recent Developments in Modeling and Applications in Statistics pp 169–177. https://doi.org/10.1007/978-3-642-32419-2_18 Nagao H (1973) On some test criteria for covariance matrix. Ann Stat 1(4):700–709. https://doi.org/10.2307/2958313 Nirmalakumari K, Rajaguru H, Rajkumar P (2020) Inference on the shape of elliptical distributions based on the mcd. Int J Imaging Syst Technol pp 1–21. https://doi.org/10.1002/ima.22431 Pavlenko T, Björkström A, Tillander A (2012) Covariance structure approximation via glasso in high-dimensional supervised classification. J Appl Stat 39(8):1643–1666 Qi Y, Wang F, Zhang L (2019) Limiting distributions of likelihood ratio test for independence of components for high-dimensional normal vectors. Ann Inst Stat Math 71:911–946. https://doi.org/10.1007/s10463-018-0666-9 Qiu Y, Chen S (2012) Test for bandedness of high-dimensional covariance matrices and bandwidth estimation. Ann Stat 40(3):1285–1314. https://doi.org/10.1214/12-AOS1002 Rahman MA, Muniyandi RC (2018) Feature selection from colon cancer dataset for cancer classification using artificial neural network. Int J Adv Sci Eng Inform Technol 8(4–2):1387–1393 Schott JR (2005) Testing for complete independence in high dimensions. Biometrika 92(4):951–956. https://doi.org/10.1093/biomet/92.4.951 Silva IR, Zhuang Y, Junior JCAdS (2021) Kronecker delta method for testing independence between two vectors in high-dimension. Stat Pap (Berl) pp 1–23. https://doi.org/10.1007/s00362-021-01238-z Srivastava M (2005) Some tests concerning the covariance matrix in high-dimensional data. J Japan Stat Soc 35(2):251–272. https://doi.org/10.14490/jjss.35.251 Srivastava M, Reid N (2012) Testing the structure of the covariance matrix with fewer observations than the dimension. J Multivar Anal 112:156–171. https://doi.org/10.1016/j.jmva.2012.06.004 Wang Q, Yao J (2013) On the sphericity test with large-dimensional observations. Electron J Stat 7:2164–2192. https://doi.org/10.1214/13-EJS842 Wang X, Xu G, Zheng S (2022) Adaptive tests for bandedness of high-dimensional covariance matrices arXiv:2204.11155 [stat.ME] Xiao H, Wu W (2013) Asymptotic theory for maximum deviations of sample covariance matrix estimates. Stochastic Processes and Their Appl 123(7):2899–2920. https://doi.org/10.1016/j.spa.2013.03.012 Xu K (2017) Testing diagonality of high-dimensional covariance matrix under non-normality. J Stat Comput Simul 87(16):3208–3224. https://doi.org/10.1080/00949655.2017.1362405 Xu K, Hao X (2019) A nonparametric test for block-diagonal covariance structure in high dimension and small samples. J Multivar Anal 173:551–567. https://doi.org/10.1016/j.jmva.2019.05.001 Yamada Y, Hyodo M, Nishiyama T (2017) Testing block-diagonal covariance structure for high-dimensional data under non-normality. J Multivar Anal 155:305–316. https://doi.org/10.1016/j.jmva.2016.12.009 Yang Y, Pan G (2015) Independence test for high dimensional data based on regularized canonical correlation coefficients. Ann Stat 43(2):467–500. https://doi.org/10.1214/14-AOS1284 Yata K, Aoshima M (2016) High-dimensional inference on covariance structures via the extended cross-data-matrix methodology. J Multivar Anal 151:151–166. https://doi.org/10.1016/j.jmva.2016.07.011 Yu K, Li Q, Bergen AW et al (2009) Pathway analysis by adaptive combination of p-values. Genet Epidemiol 33(8):700–709. https://doi.org/10.1002/gepi.20422 Zhang W, Jin B, Bai Z (2021) Learning block structures in u-statistic based matrices. Biometrika 108(4):933–946. https://doi.org/10.1093/biomet/asaa099 Zhang X, Cheng G (2014) Bootstrapping high dimensional time series. statistics arXiv:1406.1037 [math.ST] Zheng S, He X, Guo J (2022) Hypothesis testing for block-structured correlation for high dimensional variables. Statistica Sinica 32. https://doi.org/10.5705/ss.202019.0319 Zhu Z, Kay SM (2016) The Rao test for testing bandedness of complex-valued covariance matrix. In: 2016 IEEE International Conference On Acoustics, Speech and Signal Processing (ICASSP). IEEE, Shanghai, China, pp 3960–3963, https://doi.org/10.1109/ICASSP.2016.7472420