Mean Equality Tests for High-Dimensional and Higher-Order Data with k-Self Similar Compound Symmetry Covariance Structure
| dc.contributor.author | Leiva, Ricardo | |
| dc.contributor.author | Roy, Anuradha | |
| dc.date.accessioned | 2022-02-24T14:50:15Z | |
| dc.date.available | 2022-02-24T14:50:15Z | |
| dc.date.issued | 2022-02-01 | |
| dc.date.updated | 2022-02-24T14:50:16Z | |
| dc.description.abstract | An extension of the D2 test statistic to test the equality of mean for high-dimensional and k-th order array-variate data using k-self similar compound symmetry (k-SSCS) covariance structure is derived. The k-th order data appear in many scientific fields including agriculture, medical, environmental and engineering applications. We discuss the property of this k-SSCS covariance structure, namely, the property of Jordan algebra. We formally show that our D2 test statistic for k-th order data is an extension or the generalization of the D2 test statistic for second-order data and for third-order data, respectively. We also derive the D2 test statistic for third-order data and illustrate its application using a medical dataset from a clinical trial study of the eye disease glaucoma. The new test statistic is very efficient for high-dimensional data where the estimation of unstructured variance-covariance matrix is not feasible due to small sample size. | |
| dc.description.department | Management Science and Statistics | |
| dc.identifier | doi: 10.3390/sym14020291 | |
| dc.identifier.citation | Symmetry 14 (2): 291 (2022) | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12588/803 | |
| dc.rights | Attribution 4.0 United States | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | array-variate data | |
| dc.subject | eigenblock | |
| dc.subject | high dimensional data | |
| dc.subject | Wishart distribution | |
| dc.subject | Hotelling’s T2 statistic | |
| dc.subject | Lawley-Hotelling trace distribution | |
| dc.title | Mean Equality Tests for High-Dimensional and Higher-Order Data with k-Self Similar Compound Symmetry Covariance Structure | |
| dc.type | Article | en_US |