Consistent Estimation in General Sublinear Preferential Attachment Trees

TL;DR

This paper introduces a consistent empirical estimator for the preferential attachment function in general trees, using a branching process framework, and validates it through simulations.

Contribution

It presents a novel estimator for the attachment function in preferential attachment trees and proves its almost sure consistency.

Findings

Estimator is almost surely consistent.

Simulation results demonstrate empirical properties.

Framework applicable to general preferential attachment models.

Abstract

We propose an empirical estimator of the preferential attachment function $f$ in the setting of general preferential attachment trees. Using a supercritical continuous-time branching process framework, we prove the almost sure consistency of the proposed estimator. We perform simulations to study the empirical properties of our estimators.