TY  - JOUR
AU  - Chongcharoen, Samruam 
PY  - 2012
TI  - One-Sided Multivariate Tests for High Dimensional Data
JF  - Journal of Mathematics and Statistics
VL  - 8
IS  - 2
DO  - 10.3844/jmssp.2012.274.282
UR  - https://thescipub.com/abstract/jmssp.2012.274.282
AB  - 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p, the likelihood ratio tests of the null hypothesis that the mean vector was zero with a one-sided alternative were no longer valid because they involved with sample covariance matrix which was singular.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.