Effectiveness of bootstrap bias correction in the context of clock offset estimators

Estimating and correcting the offset between two or more clocks is an important problem in data communication networks. For example, Internet telephony depends on network routers having a common notion of time, and cellular networks provide a higher quality of service by using transmission protocols that depend on neighboring base stations knowing the offset that exists between their local clocks. In previous work it was shown that bootstrap bias correction of Paxson's well-known estimator of clock offset produces an estimator with improved bias and mean squared error (NISE) properties. In addition, the ordered-BLUE (o-BLUE) under an exponential distribution for network delays was derived, and its bootstrap bias-corrected form was shown to have lower bias and MSE than the bootstrap bias-corrected form of Paxson's estimator when network delays follow lognormal, gamma, and Weibull distributions. The inferred robustness of the bias-corrected o-BLUE to the assumed distribution of network delays is an attractive property, because no single family of distributions can consistently characterize network delays. Recent Internet traffic modeling research has suggested that the Pareto distribution is an applicable distribution for network delays. That finding motivates the work in this article concerned with clock offset estimation and the effectiveness of bootstrap bias-corrected estimators in the context of heavy-tailed network delays. An important result is the demonstrated robustness of the bias-corrected form of Paxson's estimator in the presence of heavy-tailed network delays. An additional and somewhat surprising result is that if network delays follow a Pareto distribution, then bootstrap bias correction of the exponential o-BLUE fails in the sense that the absolute bias increases. The same finding is observed in an alternative class of heavy-tailed distributions, where the success or failure of bootstrap bias correction is traceable to a parameter that reflects the weight of the tail. Although it is well known that bias correction can increase MSE, to the best of our knowledge no practical application in which it increases the absolute bias has been identified up to this point.