A high-dimensional test for the k-sample Behrens–Fisher problem

References

• Aoshima, M., and Yata, K. (2011), ‘Two-stage Procedures for High-dimensional Data’, Sequential Analysis, 30, 356–399.
   Web of Science ®Google Scholar
• Bai, Z., and Saranadasa, H. (1996), ‘Effect of High Dimension: By An Example of a Two Sample Problem’, Statistica Sinica, 6, 311–329.
   Web of Science ®Google Scholar
• Cai, T.T., and Xia, Y. (2014), ‘High-dimensional Sparse MANOVA’, Journal of Multivariate Analysis, 131, 174–196.
   Web of Science ®Google Scholar
• Cao, M., Liang, S., He, D., and Xu, K. (2022), ‘Testing Linear Hypothesis of High-dimensional Means with Unequal Covariance Matrices’, Journal of the Korean Statistical Society, 51, 526–541.
   Web of Science ®Google Scholar
• Cao, M., Park, J., and He, D. (2019), ‘A Test for the k Sample Behrens-Fisher Problem in High Dimensional Data’, Journal of Statistical Planning and Inference, 201, 86–102.
   Web of Science ®Google Scholar
• Chen, S., Li, J., and Zhong, P. (2019), ‘Two-sample and ANOVA Tests for High Dimensional Means’, The Annals of Statistics, 47, 1443–1474.
   Web of Science ®Google Scholar
• Chen, S., and Qin, Y. (2010), ‘A Two-sample Test for High-dimensional Data with Applications to Gene-set Testing’, The Annals of Statistics, 38, 808–835.
   Web of Science ®Google Scholar
• Feng, L., Zou, C., Wang, Z., and Zhu, L. (2015), ‘Two Sample Behrens-Fisher Problem for High-dimensional Data’, Statistica Sinica, 25, 1297–1312.
   Web of Science ®Google Scholar
• Ghosh, A., and Biswas, M. (2016), ‘Distribution-free High-dimensional Two-sample Tests Based on Discriminating Hyperplanes’, Test, 25, 525–547.
   Web of Science ®Google Scholar
• Hotelling, H. (1931), ‘The Generalization of Student's Ratio’, The Annals of Mathematical Statistics, 2, 360–378.
   Google Scholar
• Hu, J., Bai, Z., Wang, C., and Wang, W. (2017), ‘On Testing the Equality of High Dimensional Mean Vectors with Unequal Covariance Matrices’, Annals of the Institute of Statistical Mathematics, 69, 365–387.
   Web of Science ®Google Scholar
• Locantore, N., Marron, J.S., Simpson, D.G., Tripoli, N., Zhang, J.T., Cohen, K.L., Boente, G., Fraiman, R., Brumback, B., Croux, C., Fan, J., Kneip, A., Marden, J.I., Peã, D., Prieto, J., Ramsay, J.O., Valderrama, M.J., Aguilera, A.M., Locantore, N., Marron, J.S., Simpson, D.G., Tripoli, N., Zhang, J.T., and Cohen, K.L. (1999), ‘Robust Principal Component Analysis for Functional Data’, Test, 8, 1–73.
   Web of Science ®Google Scholar
• Ma, Y., Lan, W., and Wang, H. (2015), ‘A High Dimensional Two-sample Test Under a Low Dimensional Factor Structure’, Journal of Multivariate Analysis, 140, 162–170.
   Web of Science ®Google Scholar
• Park, J., and Ayyala, D. (2013), ‘A Test for the Mean Vector in Large Dimension and Small Samples’, Journal of Statistical Planning and Inference, 143, 929–943.
   Web of Science ®Google Scholar
• Schott, J. (2007), ‘Some High-dimensional Tests for a One-way MANOVA’, Journal of Multivariate Analysis, 98, 1825–1839.
   Web of Science ®Google Scholar
• Srivastava, M. (2009), ‘A Test for the Mean Vector with Fewer Observations Than the Dimension Under Non-normality’, Journal of Multivariate Analysis, 100, 518–532.
   Web of Science ®Google Scholar
• Srivastava, M., and Du, M. (2008), ‘A Test for the Mean Vector with Fewer Observations Than the Dimension’, Journal of Multivariate Analysis, 99, 386–402.
   Web of Science ®Google Scholar
• Srivastava, M., Katayama, S., and Kano, Y. (2013), ‘A Two Sample Test in High Dimensional Data’, Journal of Multivariate Analysis, 114, 349–358.
   Web of Science ®Google Scholar
• Xu, K. (2017), ‘A New Nonparametric Test for High-dimensional Regression Coefficients’, Journal of Statistical Computation and Simulation, 87, 855–869.
   Web of Science ®Google Scholar
• Xu, K., Tian, Y., and He, D. (2021), ‘A High Dimensional Nonparametric Test for Proportional Covariance Matrices’, Journal of Multivariate Analysis, 184, 104762.
   Google Scholar
• Yamada, T., and Himeno, T. (2015), ‘Testing Homogeneity of Mean Vectors Under Heteroscedasticity in High-dimension’, Journal of Multivariate Analysis, 139, 7–27.
   Web of Science ®Google Scholar
• Zhang, J. (2005), ‘Approximate and Asymptotic Distributions of Chi-squared-type Mixtures with Applications’, Journal of the American Statistical Association, 100, 273–285.
   Web of Science ®Google Scholar
• Zhang, J., Guo, J., Zhou, B., and Cheng, M. (2020), ‘A Simple Two-sample Test in High Dimensions Based on L2-norm’, Journal of the American Statistical Association, 115, 1011–1027.
   Web of Science ®Google Scholar
• Zhang, J., Zhou, B., Guo, J, and Zhu, T. (2021), ‘Two-sample Behrens-Fisher Problems for High-dimensional Data: A Normal Reference Approach’, Journal of Statistical Planning and Inference, 213, 142–161.
   Web of Science ®Google Scholar
• Zhou, B., Guo, J, and Zhang, J. (2017), ‘High-dimensional General Linear Hypothesis Testing Under Heteroscedasticity’, Journal of Statistical Planning and Inference, 188, 36–54.
   Web of Science ®Google Scholar
• Zhou, C., and Kong, X. (2015), ‘Testing of High Dimensional Mean Vectors Via Approximate Factor Model’, Journal of Statistical Planning and Inference, 167, 216–227.
   Web of Science ®Google Scholar