The abstract of doctoral dissertation ‘Some research on hypothesis testing and nonparametric variable screening problems for high dimensional data’ - Yongshuai Chen; Hengjian Cui (Statistical Theory and Related Fields, 2020)
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.