Optimal Component Selection in High Dimensions
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It is now the modern trend and reality in various fields of life and science that the data sets to be analyzed are high dimensional, and the number of observations is much smaller than their dimension. As the classical statistical methods are not designed to deal with big or high-dimensional data, the problem of developing new methods of high-dimensional statistical analysis is very important. In this thesis, we study the problem of component or variable selection in a normal mixture model based on a single high-dimensional observation. The goal is to examine the possibilities and limitations of optimal component selection in a two-point normal mixture model and, whenever possible, to construct optimal selection procedures. In addition to that, the problem of estimating an unknown parameter that determines the sparsity pattern of the data is addressed.
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Copyright © 2014 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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- 2014
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cui-optimalcomponentselectioninhighdimensions.pdf | 2023-05-04 | Public | Download |