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Test on the linear combinations of mean vectors in high-dimensional data

Huiqin Li (), Jiang Hu (), Zhidong Bai (), Yanqing Yin () and Kexin Zou ()
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Huiqin Li: Jiangsu Normal University
Jiang Hu: Northeast Normal University
Zhidong Bai: Northeast Normal University
Yanqing Yin: Jiangsu Normal University
Kexin Zou: Northeast Normal University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, vol. 26, issue 1, 188-208

Abstract: Abstract In this study, we propose a procedure for simultaneous testing $$l (l\ge 1)$$ l ( l ≥ 1 ) linear relations on $$k(k\ge 2)$$ k ( k ≥ 2 ) high-dimensional mean vectors with heterogeneous covariance matrices, which extends the result derived by Nishiyama et al. (J Stat Plan Inference 143(11):1898–1911, 2013) and does not need the normality assumption. The newly proposed test statistic is motivated by Bai and Saranadasa (Statistica Sinica 6(2):311–329, 1996) and Chen and Qin (Ann Stat 38(2):808–835, 2010). As a special case, our result could be applied to multivariate analysis of variance, that is, testing the equality of k high-dimensional mean vectors.

Keywords: Hypothesis test; High-dimensional data; Mean vectors; Bonferroni correction; Primary 62H15; Secondary 62E20 (search for similar items in EconPapers)
Date: 2017
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