## Abstract

We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log-transformed squared t-statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Simulation studies and a real data analysis are also carried out to demonstrate the advantages of our likelihood ratio test methods.

Original language | English |
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Pages (from-to) | 256-267 |

Number of pages | 12 |

Journal | Biometrics |

Volume | 75 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2019 |

## Scopus Subject Areas

- Statistics and Probability
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

## User-Defined Keywords

- high-dimensional data
- Hotelling's test
- Likelihood ratio test
- log-transformed squared t-statistic
- statistical power
- type I error