Fourier Approach of Inverse Regression Estimate in Sufficient Dimension Reduction (304703)*Jiaying Weng, University of Kentucky
Xiangrong Yin, University of Kentucky
Keywords: Centra subspace, Fourier transform, Sufficient dimension reduction, Variable selection, Predictors hypothesis tests.
We develop an optimal inverse regression estimate using Fourier transform, Fourier transform inverse regression estimator (FT-IRE). Most inverse dimension reduction techniques require the number of slices, which could be problematic. Using Fourier transform avoid this problem. The degenerate and robust Fourier transform inverse regression estimates are also introduced for less computational and robust cases. Along the line, the group LASSO is used for variable selection. Asymptotic properties and the marginal dimension and conditional predictors hypothesis tests are studied. Various simulations studies and a real data analysis of Australian Institute of Sport are used to demonstrate the advantages of our proposed methods.