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

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