Journal of Mathematics and Statistics

One-Sided Multivariate Tests for High Dimensional Data

Samruam Chongcharoen

DOI : 10.3844/jmssp.2012.274.282

Journal of Mathematics and Statistics

Volume 8, Issue 2

Pages 274-282


Problem statement: For a multivariate normal population with size smaller than dimension, n<p, the likelihood ratio tests of the null hypothesis that the mean vector was zero with a one-sided alternative were no longer valid because they involved with sample covariance matrix which was singular. Approach: The test statistics for one-sided multivariate hypotheses with n<p were proposed. Results: The simulation study showed that the proposed tests provided reasonable type I error rate for one-sided covariance structures. They also give good powers. The application of these tests was given by testing of one-sided hypotheses on DNA micro array data. Conclusion: Under that there have no such other tests available at present for this kind of hypothesis testing with n<p yet, the proposed tests are good ones. However, the methodology is valid for any one-sided hypotheses application which involves high-dimensional data.


© 2012 Samruam Chongcharoen. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.