Explicit Maximum Likelihood Loss Estimator in Multicast Tomography

TL;DR

This paper introduces an explicit maximum likelihood estimator for multicast tomography that approximates the true MLE without iterative methods, improving estimation accuracy for finite sample sizes.

Contribution

It presents a novel explicit MLE estimator for multicast tomography, addressing limitations of previous estimators that were not true MLEs, especially for finite samples.

Findings

The explicit MLE estimator closely approximates the true MLE.

Comparison shows the new estimator reduces bias compared to previous methods.

The estimator improves estimation accuracy in multicast network tomography.

Abstract

For the tree topology, previous studies show the maximum likelihood estimate (MLE) of a link/path takes a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since then, the main concern is focused on searching for methods to solve the high degree polynomial without using iterative approximation. An explicit estimator based on the Law of Large Numbers has been proposed to speed up the estimation. However, the estimate obtained from the estimator is not a MLE. When $n<\infty$, the estimate may be noticeable different from the MLE. To overcome this, an explicit MLE estimator is presented in this paper and a comparison between the MLE estimator and the explicit estimator proposed previously is presented to unveil the insight of the MLE estimator and point out the pitfall of the previous one.