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

Huiqin Li, Jiang Hu, Zhidong Bai, Yanqing Yin, Kexin Zou

• 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.