PhD Candidate, The University of Georgia Department of Statistics
This dissertation undertakes the theory and methods of sufficient dimension reduction in the content of Hilbert-Schmidt Independence Criterion (HSIC). The proposed estimation methods enjoy model free property and require no link function to be smoothed or estimated. Two tests: Permutation test and Bootstrap test, are investigated to examine the true underlying dimension of data considered. Sampling distribution of our estimator is established in single-index regressions. Root-n consistency of our estimator is proved for multiple-index models.