# Mean vector testing for high-dimensional dependent observations

*Deepak Nag Ayyala*,
*Junyong Park* and
*Anindya Roy*

*Journal of Multivariate Analysis*, 2017, vol. 153, issue C, 136-155

**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.

**Keywords:** High-dimension; Asymptotic normality; Triangular array; Dependent data; Mean vector testing (search for similar items in EconPapers)

**Date:** 2017

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