Sufficient dimension reduction for complex data structures
2014-06
Loading...
View/Download File
Persistent link to this item
Statistics
View StatisticsJournal Title
Journal ISSN
Volume Title
Title
Sufficient dimension reduction for complex data structures
Authors
Published Date
2014-06
Publisher
Type
Thesis or Dissertation
Abstract
Data with complex structures, such as array-valued predictors, or responses, are commonly encountered in modern statistical applications. Such data typically contain intrinsic relationship among the entries of each array-valued variable. Conventional sufficient dimension reduction (SDR) methods cannot efficiently utilize the data structures and are inappropriate for the complex data. In this thesis, we propose a class of sufficient dimension reduction methods, including model-based dimension reduction methods: dimension folding principal component analysis (PCA) and dimension folding principal fitted components (PFC), moment-based sufficient dimension reduction methods: tensor sliced inverse regression (SIR), and envelope methods to tackle data with array-valued predictors, or responses. The proposed methods can simultaneously reduce a predictor's, or a response's, multiple dimensions without losing any information in prediction or classification. We study the asymptotic properties of these methods and demonstrate their efficiency in both theoretical and numerical studies.
Description
University of Minnesota Ph.D. dissertation. June 2014. Major: Statistics. Advisor: Ralph Dennis Cook. 1 computer file (PDF); xi, 132 pages.
Related to
Replaces
License
Collections
Series/Report Number
Funding information
Isbn identifier
Doi identifier
Previously Published Citation
Suggested citation
Ding, Shanshan. (2014). Sufficient dimension reduction for complex data structures. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/164799.
Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.