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Title: Estimation of the relative scale of trees from their Harris path Authors:  Romain Azais - INRIA Nancy (France) [presenting]
Alexandre Genadot - University of Bordeaux (France)
Benoit Henry - University of Lorraine (France)
Abstract: Hierarchical data naturally appear in various application fields, e.g., plant modeling and XML file analysis. The aim is to propose a new method to estimate the relative scale of ordered trees relying on a theoretical study for Galton-Watson trees conditioned on their number of nodes. Our approach is based on the adequacy of the Harris path of the tree with an expected function that describes the average shape of the tree. We prove the consistency of our estimators for conditioned Galton-Watson trees and compare them with a previous approach of the literature. Numerical investigations show the good behavior of our procedure on finite-sample sizes as well as from missing or noisy data. An application to the analysis of revisions of Wikipedia articles is also considered and states the robustness of our approach.