### Abstract

When testing for the mean vector in a high-dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve type I error at a given nominal significance level. We propose a new test for the mean vector when the dimension increases linearly with sample size and the data is a realization of an M-dependent stationary process. The order M is also allowed to increase with the sample size. Asymptotic normality of the test statistic is derived by extending the Central Limit Theorem for M-dependent processes using two-dimensional triangular arrays. The cost of ignoring dependence among observations is assessed in finite samples through simulations.

Original language | English (US) |
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Pages (from-to) | 136-155 |

Number of pages | 20 |

Journal | Journal of Multivariate Analysis |

Volume | 153 |

DOIs | |

State | Published - Jan 1 2017 |

Externally published | Yes |

### Keywords

- Asymptotic normality
- Dependent data
- High-dimension
- Mean vector testing
- Triangular array

### ASJC Scopus subject areas

- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty

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## Cite this

*Journal of Multivariate Analysis*,

*153*, 136-155. https://doi.org/10.1016/j.jmva.2016.09.012