Nonparametric High-Dimensional Multi-Sample Tests based on Graph Theory

References

• 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
• Benjamini, Y., and Hochberg, Y. (2014), “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing,” Journal of the Royal Statistical Society, Series B, 57, 289–300. DOI: 10.1111/j.2517-6161.1995.tb02031.x.
   Google Scholar
• Biswas, M., Mukhopadhyay, M., and Ghosh, A. K. (2014), “A Distribution-Free Two-Sample Run Test Applicable to High-Dimensional Data,” Biometrika, 101, 913–926. DOI: 10.1093/biomet/asu045.
   Web of Science ®Google Scholar
• Cai, T., Liu, W., and Xia, Y. (2014), “Two-Sample Test of High Dimensional Means Under Dependence,” Journal of the Royal Statistical Society, Series B, 76, 349–372. DOI: 10.1111/rssb.12034.
   Google Scholar
• Chen, H., Chen, X., and Su, Y. (2018), “A Weighted Edge-Count Two Sample Test for Multivariate and Object Data,” Journal of the American Statistical Association: Theory and Methods, 113, 1146–1155. DOI: 10.1080/01621459.2017.1307757.
   Web of Science ®Google Scholar
• Chen, H., and Friedman, J. H. (2017), “A New Graph-based Two-Sample Test for Multivariate and Object Data,” Journal of the American Statistical Association: Theory and Methods, 112, 397–409. DOI: 10.1080/01621459.2016.1147356.
   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,” Annals of Statistics, 38, 808–835.
   Web of Science ®Google Scholar
• Friedman, J. H., and Rafsky, L. C. (1979), “Multivariate Generalizations of the Wald-Wolfowitz and Smirnov Two-Sample Tests,” Annals of Statistics, 7, 697–717.
   Web of Science ®Google Scholar
• Genz, A. (1992), “Numerical Computation of Multivariate Normal Probabilities,” Journal of Computational and Graphical Statistics, 1, 141–150. DOI: 10.1080/10618600.1992.10477010.
   Google Scholar
• Jung, W. B., Shim, H. J., and Kim, S. G. (2019), “Mouse BOLD fMRI at Ultrahigh Field Detects Somatosensory Networks Including Thalamic Nuclei,” NeuroImage, 195, 203–214. DOI: 10.1016/j.neuroimage.2019.03.063.
   PubMed Web of Science ®Google Scholar
• Mukhopadhyay, S., and Wang, K. (2020), “A Nonparametric Approach to High-Dimensional k-sample Comparison Problems,” Biometrika, 107, 555–572. DOI: 10.1093/biomet/asaa015.
   Web of Science ®Google Scholar
• Shalon, D., Smith, S. J., and Brown, P. O. (1996), “A DNA Microarray System for Analyzing ComplexDNA Samples Using Two-Color Fluorescent Probehybridization,” Genome Research, 6, 639–645. DOI: 10.1101/gr.6.7.639.
   PubMed Web of Science ®Google Scholar
• Shi, X., Wu, Y., and Rao, C. R. (2017), “Consistent and Powerful Graph-based Change-Point Test for High-Dimensional Data,” Proceedings of the National Academy of Sciences, 114, 3969–3974. DOI: 10.1073/pnas.1702654114.
   PubMed Web of Science ®Google Scholar
• ——— (2018), “Consistent and Powerful non-Euclidean Graph-based Change-Point Test with Applications to Segmenting Random Interfered Video Data,” Proceedings of the National Academy of Sciences, 115, 5914–5919.
   PubMed Web of Science ®Google Scholar
• Székely, G. J., and Rizzo, M. L. (2015), “Hierarchical Clustering via Joint between-within Distances: Extending Ward’s Minimum Variance Method,” Journal of Classification, 22, 151–183. DOI: 10.1007/s00357-005-0012-9.
   Google Scholar
• Wald, A., and Wolfowitz, J. (1940), “On a Test Whether Two Samples are from the Same Distribution,” Annals of Mathematical Statistics, 11, 147–162. DOI: 10.1214/aoms/1177731909.
   Google Scholar
• Weinstein, J. N., Collisson, E. A., Mills, G. B., Shaw, K. R., Ozenberger, B. A., Ellrott, K., Shmulevich, I., Sander, C., and Stuart, J. M. (2013), “The Cancer Genome Atlas Pan-Cancer Analysis Project,” Nature Genetics, 45, 1113–1120. DOI: 10.1038/ng.2764.
   PubMed Web of Science ®Google Scholar
• Xu, G., Lin, L., Wei, P., and Pan, W. (2016), “An Adaptive Two-Sample Test for High-Dimensional Means,” Biometrika, 103, 609–624. DOI: 10.1093/biomet/asw029.
   PubMed Web of Science ®Google Scholar
• Zhang, J., and Chen, H. (2021), “Graph-based Two-Sample Tests for Data with Repeated Observations,” Statistica Sinica, to appear. DOI: 10.5705/ss.202019.0116.
   Web of Science ®Google Scholar