Loss Rate Estimators and the Properties for the Tree Topology

TL;DR

This paper introduces new explicit loss rate estimators for tree-structured networks, proves their unbiasedness and consistency, and provides formulas to compare their variances, aiding in optimal estimator selection.

Contribution

It develops a comprehensive set of explicit estimators with proven statistical properties and derives variance formulas to rank and select the most efficient estimator for loss tomography.

Findings

All proposed estimators are unbiased and consistent.

Variance formulas enable ranking of estimators.

Identification of errors in previous estimation methods.

Abstract

A large number of explicit estimators are proposed in this paper for loss rate estimation in a network of the tree topology. All of the estimators are proved to be unbiased and consistent instead of asymptotic unbiased as that obtained in [1] for a specific estimator. In addition, a set of formulae are derived for the variances of various maximum likelihood estimators that unveil the connection between the path of interest and the subtrees connecting the path to observers. Using the formulae, we are able to not only rank the estimators proposed so far, including those proposed in this paper, but also identify the errors made in previous works. More importantly, using the formulae we can easily identify the most efficient explicit estimator from a pool that makes model selection feasible in loss tomography