An Inferential Perspective on Data Depth
2017-05
Loading...
View/Download File
Persistent link to this item
Statistics
View StatisticsJournal Title
Journal ISSN
Volume Title
Title
An Inferential Perspective on Data Depth
Authors
Published Date
2017-05
Publisher
Type
Thesis or Dissertation
Abstract
Data depth provides a plausible extension of robust univariate quantities like ranks, order statistics and quantiles in multivariate setup. Although depth has gained visibility and has seen many applications in recent years, especially in classification problems for multivariate and functional data, its generalizability and utility in achieving traditional parametric inferential goals is largely unexplored. In this thesis we develop several approaches to address this. In particular, firstly we define an evaluation map function that is more general than data depth, and establish several results in a parametric modelling context using a broad definition of a statistical model. A fast algorithm for covariate selection using data depths as evaluation functions arises as a special case of this. We demonstrate applications of this framework on data from diverse fields: namely climate science, medical imaging and behavioral genetics. Secondly we propose a multivariate rank transformation using data depth and use them for robust inference in location and scale problems in elliptical distributions. Thirdly, we lay out a depth-based regularization framework in multi-response regression, and derive a new method of nonconvex penalized sparse regression in the multitask situation. Across the thesis, several simulation studies and real data examples demonstrate the effectiveness of the methods developed here.
Description
University of Minnesota Ph.D. dissertation. May 2017. Major: Statistics. Advisor: Snigdhansu Chatterjee. 1 computer file (PDF); xiii, 187 pages.
Related to
Replaces
License
Collections
Series/Report Number
Funding information
Isbn identifier
Doi identifier
Previously Published Citation
Other identifiers
Suggested citation
Majumdar, Subhabrata. (2017). An Inferential Perspective on Data Depth. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/188932.
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.