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October 2007 Object oriented data analysis: Sets of trees
Haonan Wang, J. S. Marron
Ann. Statist. 35(5): 1849-1873 (October 2007). DOI: 10.1214/009053607000000217


Object oriented data analysis is the statistical analysis of populations of complex objects. In the special case of functional data analysis, these data objects are curves, where standard Euclidean approaches, such as principal component analysis, have been very successful. Recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly non-Euclidean spaces, such as Lie groups and symmetric spaces, or of strongly non-Euclidean spaces, such as spaces of tree-structured data objects. These new contexts for object oriented data analysis create several potentially large new interfaces between mathematics and statistics. This point is illustrated through the careful development of a novel mathematical framework for statistical analysis of populations of tree-structured objects.


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Haonan Wang. J. S. Marron. "Object oriented data analysis: Sets of trees." Ann. Statist. 35 (5) 1849 - 1873, October 2007.


Published: October 2007
First available in Project Euclid: 7 November 2007

zbMATH: 1126.62002
MathSciNet: MR2363955
Digital Object Identifier: 10.1214/009053607000000217

Primary: 62H99
Secondary: 62G99

Keywords: Functional data analysis , nonlinear data space , Object oriented data analysis , population of tree-structured objects , Principal Component Analysis

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.35 • No. 5 • October 2007
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