Object oriented data analysis: sets of trees.

*(English)*Zbl 1126.62002Summary: 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 components 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.

##### MSC:

62A01 | Foundations and philosophical topics in statistics |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62H05 | Characterization and structure theory for multivariate probability distributions; copulas |

62H99 | Multivariate analysis |

62G99 | Nonparametric inference |

##### Keywords:

functional data analysis; nonlinear data space; population of tree-structured objects; principal component analysis; blood vessel data##### Software:

fda (R)##### References:

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