Inference for conditioned Galton-Watson trees from their Harris path

TL;DR

This paper introduces new estimators for the scale parameter of conditioned Galton-Watson trees, demonstrating their consistency and effectiveness through simulations and real data application in Wikipedia article revisions.

Contribution

The paper proposes novel estimators for the scale parameter of conditioned Galton-Watson trees and compares them with existing methods, showing improved finite-sample performance.

Findings

New estimators are consistent for the scale parameter.

Simulation results show good finite-sample behavior.

Application to Wikipedia data demonstrates practical utility.

Abstract

Tree-structured data naturally appear in various fields, particularly in biology where plants and blood vessels may be described by trees, but also in computer science because XML documents form a tree structure. This paper is devoted to the estimation of the relative scale parameter of conditioned Galton-Watson trees. New estimators are introduced and their consistency is stated. A comparison is made with an existing approach of the literature. A simulation study shows the good behavior of our procedure on finite-sample sizes and from missing or noisy data. An application to the analysis of revisions of Wikipedia articles is also considered through real data.