Abstract

In this thesis, we construct test statistic for association test and independence test in high dimension, respectively, and study the corresponding theoretical properties under some regularity conditions. Meanwhile, we propose a nonparametric variable screening procedure for sparse additive model with multivariate response in untra-high dimension and established some screening properties.

References

1. Escoufier, Y. (1973). Le traitement des variables vectorielles. Biometrics, 29(4), 751–760. https://doi.org/10.2307/2529140 [Crossref], [Google Scholar]
2. Fan, J., Feng, Y., & Song, R. (2011). Nonparametric independence screening in sparse ultra-high-dimensional additive models. Journal of the American Statistical Association, 106, 544–557. https://doi.org/10.1198/jasa.2011.tm09779 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
3. Fan, J., Liao, Y., & Yao, J. (2015). Power enhancement in high-dimensional cross-sectional tests. Econometrica, 83(4), 1497–1541. https://doi.org/10.3982/ECTA12749 [Crossref], [Web of Science ®], [Google Scholar]
4. Li, W., Chen, J., & Yao, J. (2017). Testing the independence of two random vectors where only one dimension is large. Statistics, 51(1), 141–153. https://doi.org/10.1080/02331888.2016.1266988 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
5. Srivastava, M. S., & Reid, N. (2012). Testing the structure of the covariance matrix with fewer observations than the dimension. Journal of Multivariate Analysis, 112, 156–171. https://doi.org/10.1016/j.jmva.2012.06.004 [Crossref], [Web of Science ®], [Google Scholar]
6. Székely, G. J., & Rizzo, M. L (2013). The distance correlation t-test of independence in high dimension. Journal of Multivariate Analysis, 117, 193–213. https://doi.org/10.1016/j.jmva.2013.02.012 [Crossref], [Web of Science ®], [Google Scholar]
7. Székely, G. J., Rizzo, M. L., & Bakirov, N. K. (2007). Measuring and testing independence by correlation of distances. Annals of Statistics, 35(6), 2769–2794. https://doi.org/10.1214/009053607000000505 [Crossref], [Web of Science ®], [Google Scholar]