Clarke, E. M., Henzinger, T. A., Veith, H., and Bloem, R. Handbook of Model Checking. Springer, 2018.
DasGupta, A. Asymptotic Theory of Statistics and Probability, volume 180. Springer, 2008.
Fan, J., Feng, Y., and Xia, L. A projection-based conditional dependence measure with applications to high-dimensional undirected graphical models. Journal of Econometrics, 218(1):119-139, 2020a.
Fan, J., Li, R., Zhang, C.-H., and Zou, H. Statistical Foundations of Data Science. Chapman and Hall/CRC, 2020b.
Gao, L., Fan, Y., Lv, J., and Shao, Q.-M. Asymptotic distributions of high-dimensional distance correlation inference. The Annals of Statistics, 49(4):1999-2020, 2021.
Genton, M. G. Classes of kernels for machine learning: a statistics perspective. Journal of Machine Learning Research, 2(Dec):299-312, 2001.
Gretton, A., Herbrich, R., Smola, A., Bousquet, O., and Scholkopf, B. Kernel methods for measuring independence. Journal of Machine Learning Research, 6:2075-2129, 2005.
Gretton, A., Fukumizu, K., Teo, C., Song, L., Scholkopf, B., and Smola, A. A kernel statistical test of independence. Advances in Neural Information Processing Systems, 20, 2007.
Hoeffding, W. A non-parametric test of independence. The Annals of Mathematical Statistics, pp. 546-557, 1948.
Imbens, G. W. and Rubin, D. B. Causal Inference in Statistics, Social, and Biomedical Sciences. Cambridge University Press, 2015.
Kendall, M. G. A new measure of rank correlation. Biometrika, 30(1/2):81-93, 1938.
Li, R., Zhong, W., and Zhu, L. Feature screening via distance correlation learning. Journal of the American Statistical Association, 107(499):1129-1139, 2012.
Maathuis, M., Drton, M., Lauritzen, S., and Wainwright, M. Handbook of Graphical Models. CRC Press, 2018.
Pearson, K. Notes on the history of correlation. Biometrika, 13(1):25-45, 1920.
Pfister, N., Buhlmann, P., Scholkopf, B., and Peters, J. Kernel-based tests for joint independence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 80(1):5-31, 2018.
Ramdas, A., Reddi, S. J., Poczos, B., Singh, A., and Wasserman, L. On the decreasing power of kernel and distance based nonparametric hypothesis tests in high dimensions. In Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.
Sejdinovic, D., Sriperumbudur, B., Gretton, A., and Fukumizu, K. Equivalence of distance-based and rkhs-based statistics in hypothesis testing. The Annals of Statistics, pp. 2263-2291, 2013.
Shao, X. and Zhang, J. Martingale difference correlation and its use in high-dimensional variable screening. Journal of the American Statistical Association, 109(507):1302-1318, 2014.
Spearman, C. The proof and measurement of association between two things. American Journal of Psychology, 15:72-101, 1904.
Sriperumbudur, B. K., Gretton, A., Fukumizu, K., Scholkopf, B., and Lanckriet, G. R. Hilbert space embeddings and metrics on probability measures. The Journal of Machine Learning Research, 11: 1517-1561, 2010.
Székely, G. J. and Rizzo, M. L. The distance correlation t-test of independence in high dimension. Journal of Multivariate Analysis, 117:193-213, 2013.
Székely, G. J., Rizzo, M. L., and Bakirov, N. K. Measuring and testing dependence by correlation of distances. The Annals of Statistics, 35(6):2769-2794, 2007.