Object oriented data analysis: Sets of trees
成果类型：
Article
署名作者：
Wang, Haonan; Marron, J. S.
署名单位：
Colorado State University System; Colorado State University Fort Collins; University of North Carolina; University of North Carolina Chapel Hill
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053607000000217
发表日期：
2007
页码：
1849-1873
关键词：
摘要：
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.