A0152
Title: Statistics for complex data objects - of brain structures, cell shapes and income share distributions
Authors: Sonja Greven - Humboldt University of Berlin (Germany) [presenting]
Abstract: Recent years have seen an increase in complex structured data objects that cannot be well represented by simple vectors. For such object data, the unit of observation naturally is the whole object - potentially sparsely observed and with error - examples being curve-valued, i.e., functional data, shapes, images, covariance matrices, compositions and probability densities. Functional and object data analysis aims to provide statistical methods for their analysis. Recent work will be presented that aims to transfer the flexibility and interpretability of statistical generalized additive modeling to such more complex data objects. Key ideas in our approaches are the definitions of linear or additive predictors in suitable linear spaces as well as of suitable response functions mapping to the spaces (Hilbert spaces, Riemannian manifolds or metric spaces) in which these data objects naturally live. A focus will be on running examples ranging from medicine to gender economics to illustrate all approaches.
