Statistics and Its Interface
Volume 13 (2020)
A test on linear hypothesis of $k$-sample means in high-dimensional data
Pages: 27 – 36
In this paper, a new test procedure is proposed to test a linear hypothesis of $k$-sample mean vectors in high-dimensional normal models with heteroskedasticity. The motivation is on the basis of the generalized likelihood ratio method and the Bennett transformation. The asymptotic distributions of the new test are derived under null and local alternative hypotheses under mild conditions. Simulation results show that the new test can control the nominal level reasonably and has greater power than competing tests in some cases. Moreover, numerical studies illustrate that our proposed test can also be applied to non-normal data.
High dimensional data, Linear hypothesis, $k$-sample, Generalized likelihood ratio method, Bennett transformation.
2010 Mathematics Subject Classification
Primary 62H15. Secondary 62E20.
Cao’s research is supported by the National Natural Science Foundation of China (Nos. 11601008, 11526070) and Doctor Startup Foundation of Anhui Normal University (No. 2016XJJ101).
He’s research is supported by the National Natural Science Foundation of China (No. 11201005).
Xu’s research is supported by the National Natural Science Foundation of China (No. 11471035).
Received 25 November 2018
Accepted 9 July 2019
Published 7 November 2019