Incidence weighting estimation under bipartite incidence graph sampling

TL;DR

This paper introduces a unified framework for estimation in various sampling methods using bipartite incidence graphs, enabling the development of new unbiased estimators with potential efficiency improvements.

Contribution

It develops a broad class of linear unbiased estimators based on bipartite incidence graphs, generalizing existing estimators like Horvitz-Thompson and enabling new estimator design.

Findings

Unified representation of diverse sampling methods

General class of unbiased estimators including classic ones

Potential efficiency gains demonstrated through examples

Abstract

Bipartite incidence graph sampling provides a unified representation of many sampling situations for the purpose of estimation, including the existing unconventional sampling methods, such as indirect, network or adaptive cluster sampling, which are not originally described as graph problems. We develop a large class of linear estimators based on the edges in the sample bipartite incidence graph, subjected to a general condition of design unbiasedness. The class contains as special cases the classic Horvitz-Thompson estimator, as well as the other unbiased estimators in the literature of unconventional sampling, which can be traced back to Birnbaum and Sirken (1965). Our generalisation allows one to devise other unbiased estimators, thereby providing a potential of efficiency gains in applications. Illustrations are given for adaptive cluster sampling, line-intercept sampling and simulated graphs.