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

In this study, we propose a procedure for simultaneous testing l ( l ≥ 1 ) linear relations on 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...

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Bibliographic Details
Published inTest (Madrid, Spain) Vol. 26; no. 1; pp. 188 - 208
Main Authors Li, Huiqin, Hu, Jiang, Bai, Zhidong, Yin, Yanqing, Zou, Kexin
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2017
Springer Nature B.V
Subjects
Covariance
Economics
Equality
Finance
Hypotheses
Hypothesis testing
Insurance
Management
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Multivariate analysis
Normality
Original Paper
Statistical tests
Statistical Theory and Methods
Statistics
Statistics for Business
Studies
Texts
Variance analysis
Hypothesis test
High-dimensional data
Primary 62H15
Bonferroni correction
Mean vectors
Secondary 62E20
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Summary:In this study, we propose a procedure for simultaneous testing l ( l ≥ 1 ) linear relations on 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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1133-0686
1863-8260
DOI:10.1007/s11749-016-0505-3