### 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 |

### Fingerprint

### 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

### Cite this

*Journal of Multivariate Analysis*,

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

**Mean vector testing for high-dimensional dependent observations.** / Ayyala, Deepak Nag; Park, Junyong; Roy, Anindya.

Research output: Contribution to journal › Article

*Journal of Multivariate Analysis*, vol. 153, pp. 136-155. https://doi.org/10.1016/j.jmva.2016.09.012

}

TY - JOUR

T1 - Mean vector testing for high-dimensional dependent observations

AU - Ayyala, Deepak Nag

AU - Park, Junyong

AU - Roy, Anindya

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Asymptotic normality

KW - Dependent data

KW - High-dimension

KW - Mean vector testing

KW - Triangular array

UR - http://www.scopus.com/inward/record.url?scp=84992144158&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992144158&partnerID=8YFLogxK

U2 - 10.1016/j.jmva.2016.09.012

DO - 10.1016/j.jmva.2016.09.012

M3 - Article

VL - 153

SP - 136

EP - 155

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -