Mean vector testing for high dimensional dependent observations

Deepak Nag Ayyala; Junyong Park; Anindya Roy

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arXiv · 1411.3390

Mean vector testing for high dimensional dependent observations

Deepak Nag Ayyala·Junyong Park·Anindya Roy

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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 result for M -dependent processes using two dimensional triangular arrays. Finite sample simulation results indicate the cost of ignoring dependence amongst observations.

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Deepak Nag Ayyala, Junyong Park, Anindya Roy. 2014-11-14. Mean vector testing for high dimensional dependent observations. https://arxiv.org/abs/1411.3390

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