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Mean vector testing for high-dimensional dependent observations

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  • Ayyala, Deepak Nag
  • Park, Junyong
  • Roy, Anindya

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.

Suggested Citation

  • Ayyala, Deepak Nag & Park, Junyong & Roy, Anindya, 2017. "Mean vector testing for high-dimensional dependent observations," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 136-155.
    • Handle: RePEc:eee:jmvana:v:153:y:2017:i:c:p:136-155
    DOI: 10.1016/j.jmva.2016.09.012
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    References listed on IDEAS

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    Cited by:

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