1. Anderson, T. W. (2003), An Introduction to Multivariate Statistical Analysis. New Jersey: Wiley-Interscience.
2. Bottesch, T., Bühler, T. Kächele, M. (2016), Speeding up k-means by approximating Euclidean distances via block vectors. Proceedings of the 33rd International Conference on International Conference on Machine Learning, Volume 48, 2578-2586.
3. Escoufier, Y. (1973), Le traitement des variables vectorielles. Biometrics, 29, 751-760. [
DOI:10.2307/2529140]
4. Fang, K. T., Zhang, Y. T. (1990), Generalized multivariate analysis. Springer-Verlag, Berlin; Science Press, Beijing.
5. Flexer, A., Schnitzer, D. (2015), Choosing l_p norms in high-dimensional spaces based on hub analysis. Neurocomputing, 169, 281-287. [
DOI:10.1016/j.neucom.2014.11.084]
6. Freeman, J. and Modarres, R. (2005), Efficiency of test for independence after Box-Cox transformation. Journal of Multivariate Analysis, 95, 107-118. [
DOI:10.1016/j.jmva.2004.08.005]
7. Freeman, J. and Modarres, R. (2006), Inverse Box-Cox: The power-normal distribution. Statistics and Probability Letters, 76, 764-772. [
DOI:10.1016/j.spl.2005.10.036]
8. Guo, L., Modarres, R. (2019), Interpoint Distance Classification of High Dimensional Discrete Observations. International Statistical Review, 87(2), 191-206. [
DOI:10.1111/insr.12281]
9. Guo, L., Modarres, R. (2020), Nonparametric tests of independence based on interpoint distance. Journal of Nonparametric Statistics, 32 (1), 225-245. [
DOI:10.1080/10485252.2020.1714613]
10. Gupta, A. K. and Huang, W. J. (2002), Quadratic forms in skew normal variates. J. Math. Anal. Appl., 273, 558-564.
11. Iwashita, T. and Siotani, M. (1994), Asymptotic Distributions of Functions of a Sample Covariance Matrix under the Elliptical Distribution. The Canadian Journal of Statistics, 22 (2), 273-283. [
DOI:10.2307/3315589]
12. Li, J. (2018), Asymptotic normality of interpoint distances for high-dimensional data with applications to the two-sample problem. Biometrika, 105 (3), 529-546. [
DOI:10.1093/biomet/asy020]
13. Marozzi, M. (2015), Multivariate multidistance tests for high-dimensional low sample size case-control studies. Statistics in Medicine, 34, 1511-1526. [
DOI:10.1002/sim.6418]
14. Marozzi, M. (2016), Multivariate tests based on interpoint distances with application to magnetic resonance imaging. Stat. Methods Med. Res., 25 (6), 2593-2610. [
DOI:10.1177/0962280214529104]
15. Marozzi, M., Mukherjee, A. and Kalina, J. (2020), Interpoint distance tests for high-dimensional comparison studies. J. Appl. Stat., 47 (4), 653-665. [
DOI:10.1080/02664763.2019.1649374]
16. Modarres, R. and Song, Y. (2020), Interpoint Distances: Applications, Properties and Visualization. Applied Stochastic Models in Business and Industry, [
DOI:10.1002/asmb.2508]
17. Modarres, R. (2020), Nonparametric Tests for Detection of High Dimensional Outliers. Submitted for publication.
18. Muirhead R. J. (1982), Aspects of Multivariate Statistical Theory, John Wiley & Sons, New York, NY.
19. Pal, A. K., Mondal, P. K., and Ghosh, A. K. (2016), High dimensional nearest neighbor classification based differences of inter-point distances. Pattern Recognition Letters, 74, 1-8. [
DOI:10.1016/j.patrec.2016.01.018]
20. Robert, P., Cl'eroux, R., and Ranger, N. (1985), Some results on vector correlation. Computational Statistics and Data Analysis, 3, 25-32. [
DOI:10.1016/0167-9473(85)90055-6]
21. Sarkar, S. and Ghosh, A. K. (2020), On Perfect Clustering of High Dimension, Low Sample Size Data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42(9), 2257-2272. [
DOI:10.1109/TPAMI.2019.2912599]
22. Song, Y. and Modarres, R. (2019), Interpoint Distance Test of Homogeneity for Multivariate Mixture Models. International Statistical Review, 87 (3), 613-638. [
DOI:10.1111/insr.12332]
23. Srivastava, M. S. (2005), Some tests concerning the covariance matrix in high-dimensional data. Journal of Japan Statistical Society, 35, 251-272. [
DOI:10.14490/jjss.35.251]
24. Srivastava, M. S. and Kubokawa, T. (2013), Tests for multivariate analysis of variance in high dimension under non-normality. Journal of Multivariate Analysis, 115, 204-216. [
DOI:10.1016/j.jmva.2012.10.011]