Mean vector testing for high-dimensional dependent observations

Deepak Nag Ayyala, Junyong Park, Anindya Roy

Research output: Contribution to journalArticle

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)136-155
Number of pages20
JournalJournal of Multivariate Analysis
Volume153
DOIs
StatePublished - Jan 1 2017
Externally publishedYes

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

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