2011
DOI: 10.3844/jmssp.2011.227.229
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Inversion of Covariance Matrix for High Dimension Data

Abstract: Problem statement: In the testing statistic problem for the mean vector of independent and identically distributed multivariate normal random vectors with unknown covariance matrix when the data has sample size less than the dimension n≤p, for example, the data came from DNA microarrays where a large number of gene expression levels are measured on relatively few subjects, the p×p sample covariance matrix S does not have an inverse.. Hence any statistic value involving inversio… Show more

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Cited by 3 publications
(3 citation statements)
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References 12 publications
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“…In high-dimensional data, for one population when the data has the number of variable exceed sample size (minus 1), p > n i -1, for example the data that collects from DNA microarrays technology where a large number of gene expression levels may be in the hundreds or thousands, are measured on relatively few subjects (Zhou et al, 2017), then the sample covariance matrix S i lose its full rank and will be singular, which makes S i does not have an inverse (Chongcharoen, 2011). Furthermore, for two populations when the data has the number of variable is larger than the sum of the sample sizes (minus 2), p > n 1 + n 2 -2, then the sample covariance matrix S ɶ in (7) does not have an inverse.…”
Section: Introductionmentioning
confidence: 99%
“…In high-dimensional data, for one population when the data has the number of variable exceed sample size (minus 1), p > n i -1, for example the data that collects from DNA microarrays technology where a large number of gene expression levels may be in the hundreds or thousands, are measured on relatively few subjects (Zhou et al, 2017), then the sample covariance matrix S i lose its full rank and will be singular, which makes S i does not have an inverse (Chongcharoen, 2011). Furthermore, for two populations when the data has the number of variable is larger than the sum of the sample sizes (minus 2), p > n 1 + n 2 -2, then the sample covariance matrix S ɶ in (7) does not have an inverse.…”
Section: Introductionmentioning
confidence: 99%
“…Many works have been published on hypothesis testing for means when both p and n go to infinity with the ratio p/n must remain bounded, Bai andSaranadasa (1996), Fujikoshi et al (2004); Srivastava and Fujikoshi (2006);Srivastava (2007;2009) ;Schott (2007) and Srivastava and Du (2008). In addition, when sample covariance matrix does not have an inverse, Chongcharoen (2011) proposed one way to modify a sample covariance matrix. Yahya et al (2011) proposed approach for feature selection in high dimensional data.…”
Section: Introductionmentioning
confidence: 99%
“…This can be achieved by dimensional analysis (Chongcharoen, 2011;Zaidi et al, 2010). Buckingham pi theorem is used herein to perform dimensional analysis, from which six variables (F, V, H, L, ν, ρ) and three fundamental dimensions ([M], [L], [T]) exist.…”
Section: Modeling and Simulationmentioning
confidence: 99%