Efficient Distributed Non-Asymptotic Confidence Regions Computation over Wireless Sensor Networks

TL;DR

This paper develops and compares distributed methods for computing finite-sample confidence regions in wireless sensor networks, considering network topology and data truncation effects.

Contribution

It introduces new distributed algorithms for non-asymptotic confidence region computation tailored to wireless sensor networks, analyzing their performance and robustness.

Findings

Optimal information exchange strategies depend on network topology.

Distributed methods can compute valid confidence regions with incomplete data.

Performance varies with network structure and data truncation.

Abstract

This paper considers the distributed computation of confidence regions tethered to multidimensional parameter estimation under linear measurement models. In particular, the considered confidence regions are non-asymptotic, this meaning that the number of required measurements is finite. Distributed solutions for the computation of non-asymptotic confidence regions are proposed, suited to wireless sensor networks scenarios. Their performances are compared in terms of required traffic load, both analytically and numerically. The evidence emerging from the conducted investigations is that the best solution for information exchange depends on whether the network topology is structured or unstructured. The effect on the computation of confidence regions of information diffusion truncation is also examined. In particular, it is proven that consistent confidence regions can be computed even when an incomplete set of measurements is available.