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