# Linkage Free Dual System Estimation

## TL;DR

This paper introduces a linkage-free method for dual system population estimation that relies on probabilistic linkage model parameters, eliminating the need for record classification or clerical review.

## Contribution

It establishes a theoretical relationship between probabilistic linkage parameters and dual system estimation, enabling population size estimation without record linkage classification.

## Key findings

- Estimator accuracy depends on the linkage model's discriminatory power.
- Method reduces reliance on manual record matching and clerical review.
- Accuracy is bounded by the ideal dual system estimator with perfect linkage.

## Abstract

In this paper it is shown that under certain conditions there is a relationship between the parameter estimation of the Fellegi--Sunter probabilistic linkage model and dual system estimation. This relationship can be used as the basis of an approach to population size estimation. In this case it is sufficient to estimate the parameters of the linkage model in order to obtain the population size estimate. Neither classification of the record pairs into links and non-links, nor forcing the records into a series of 1-1 matches, nor clerical review of the potential links is required. The accuracy of the proposed estimator appears to be bounded by the accuracy of the dual system estimator with perfect linkage and it diminishes as the discriminatory power of the linkage variables decreases.