Complex correlated systems can be molded by random matrices. Random matrices can be characterized by eigenvalues, which have a characteristic pattern even though the components of various complex correlated systems are very different. This phenomenon is known as universality.
Mathematical tools from random matrix theory have found important applications in high- dimensional statistics, like testing and inference about large covariance matrix, independence testing, large-dimensional PCA and factor model, high-dimensional regression analysis, and machine learning etc..
If your data set has a large number of variables compared to available sample size, where traditional multivariate statistical methods fail and dimensional reduction is not applicable. My methods will work.
Selected Journal Papers (corresponding author*)
1. Li Z. Y. and Yao J. F.* (2019). Testing for heteroscedasticity in high-dimensional regressions. Econometrics and Statistics, 9: 122-139. [link]
2. Passemier D., Li Z. Y.* and Yao J. F. (2017). On estimation of the noise variance in high-dimensional probabilistic principal component analysis. Journal of the Royal Statistical Society Series B (Statistical Methodology), 79: 51-67. [link]
3. Li Z. Y. and Tian M. Z.* (2017). A new method for dynamic clustering based on spectral analysis. Computational Economics, 50:373-392. [link]
4. Li Z. Y.* and Yao J. F. (2016). On two simple and effective procedures for high-dimensional classification of general populations. Statistical Papers, 57: 381-405. [link]
5. Yalamanchili H., Li Z. Y. , Wang P. W., Wong M. Yao J F.* and Wang J. W.* (2014). SpliceNet: recovering splicing isoform specific differential gene networks from RNA-Seq data of normal and diseased samples. Nucleic Acids Research, 42: e121. [link]
6. Li Z. Y., Liu S. B. and Tian M. Z.* (2014). Momentum effect differs across stock performances: Chinese evidence. Acta Mathematicae Applicatae Sinica, English Series, 30: 279-288. [link]