# Peer Reporting: Sampling Design and Unbiased Estimates

## TL;DR

This paper introduces a new method for estimating population proportions in social networks using peer reports, which improves accuracy and privacy.

## Contribution

The paper introduces the Activity Ratio Corrected ECM estimator (ECMac), which provides unbiased estimates in heterogeneous networks.

## Key findings

- ECMac reduces estimation error by up to 70% compared to conventional methods in simulations and real-world networks.
- ECMac provides unbiased and stable estimates even when network degrees are heterogeneous and correlated with attributes.

## Abstract

The Ego-Centric Sampling Method (ECM) leverages individual-level reports about peers to estimate population proportions within social networks, offering strong privacy protection without requiring full network data. However, the conventional ECM estimator is unbiased only under the restrictive assumption of a homogeneous network, where node degrees are uniform and uncorrelated with attributes. To overcome this limitation, we introduce the Activity Ratio Corrected ECM estimator (ECMac), which exploits network reciprocity to recast the population–proportion problem into an equivalent formulation in edge space. This reformulation relies solely on ego–peer data and explicitly corrects for degree–attribute dependencies, yielding unbiased and stable estimates even in highly heterogeneous networks. Simulations and analyses on real-world networks show that ECMac reduces estimation error by up to 70% compared with the conventional ECM. Our results establish a theoretically grounded and practically scalable framework for unbiased inference in network-based sampling designs.