Statistical Properties of Loss Rate Estimators in Tree Topology

Loss tomography has received considerable attention in recent years and a large number of estimators based on maximum likelihood (ML) or Bayesian principles have been proposed for the tree topology. In contrast, there has been no maximum likelihood estimator (MLE) proposed for the general topology although there has been enormous interest to extend the estimators proposed for the tree topology to the general one. In this paper, we propose a MLE for the general topology that consists of a divide and conquer strategy, two estimators, and an estimation order. The three components together ensure the estimate obtained for each link is the maximum likelihood one. Apart from the MLE, the statistical properties of the estimators are presented, including minimum-variance unbiasedness, consistence and asymptotically efficiency. In addition to the proof of the superiority of the proposed estimator over the previous ones, a simulation study is conducted to verify the theoretical result. Index Terms Divide and Conquer, General topology, Likelihood Equations, Loss tomography, Tree topology.