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Transforms In Sufficient Dimension Reduction And Their Applications In High Dimensional Data, Jiaying Weng
Transforms In Sufficient Dimension Reduction And Their Applications In High Dimensional Data, Jiaying Weng
Theses and Dissertations--Statistics
The big data era poses great challenges as well as opportunities for researchers to develop efficient statistical approaches to analyze massive data. Sufficient dimension reduction is such an important tool in modern data analysis and has received extensive attention in both academia and industry.
In this dissertation, we introduce inverse regression estimators using Fourier transforms, which is superior to the existing SDR methods in two folds, (1) it avoids the slicing of the response variable, (2) it can be readily extended to solve the high dimensional data problem. For the ultra-high dimensional problem, we investigate both eigenvalue decomposition and minimum …