A new test for the mean vector in large dimension and small samples

ABSTRACT

In this article, we consider the problem of testing the mean vector in the multivariate normal distribution, where the dimension p is greater than the sample size N. We propose a new test T_Block and obtain its asymptotic distribution. We also compare the proposed test with other two tests. The simulation results suggest that the performance of the new test is comparable to the existing two tests, and under some circumstances it may have higher power. Therefore, the new statistic can be employed in practice as an alternative choice.

KEYWORDS:

• High dimension
• Hotelling T² test
• Testing mean vector

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H15
• 62F05

Acknowledgments

The author wishes to thank the editor, the associate editor, and the anonymous referees for their helpful suggestions and comments which led to a substantial improvement of the original draft of this manuscript. The research was supported by the Fundamental Research Funds for the Central Universities (NO.BLX201611) and the National Natural Science Foundation of China (Grant No. 11471035).