Statistics and Its Interface

Volume 13 (2020)

Number 1

A test on linear hypothesis of $k$-sample means in high-dimensional data

Pages: 27 – 36

DOI: https://dx.doi.org/10.4310/SII.2020.v13.n1.a3

Authors

Mingxiang Cao (Department of Statistics, Anhui Normal University, Wuhu, Anhui, China)

Peng Sun (Department of Statistics, Anhui Normal University, Wuhu, Anhui, China; and KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, China)

Daojiang He (Department of Statistics, Anhui Normal University, Wuhu, Anhui, China)

Rui Wang (Department of Statistics, Beijing Institute of Technology, Beijing, China)

Xingzhong Xu (Department of Statistics, Beijing Institute of Technology, Beijing, China)

Abstract

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.

Keywords

High dimensional data, Linear hypothesis, $k$-sample, Generalized likelihood ratio method, Bennett transformation.

2010 Mathematics Subject Classification

Primary 62H15. Secondary 62E20.

Full Text (PDF format)

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