Knavoot Jiamwattanapong and Samruam Chongcharoen

pp. 477 - 484

Abstract

For the testing of the mean vector where the data are drawn from a multivariate normal population, the renowned
Hotelling’s T²
 test is no longer valid when the dimension of the data equals or exceeds the sample size. In this study, we
consider the problem of testing the hypothesis H :μ  0 and propose a new test based on the idea of keeping more
information from the sample covariance matrix. The development of the statistic is based on Hotelling’s T
2
 distribution and
the new test has invariance property under a group of scalar transformation. The asymptotic distribution is derived under
the null hypothesis. The simulation results show that the proposed test performs well and is more powerful when the data
dimension increases for a given sample size. An analysis of DNA microarray data with the new test is demonstrated. 

Keywords

• high-dimensional data
• hypothesis testing
• mean vector
• block diagonal structure