Multiple system estimation for the size of the Māori population in New Zealand

We investigate the situation where two or more registers, or lists, of individuals are linked both for the purpose of population size estimation and to investigate the relationship between variables appearing on all or only some of the registers. There is usually no full picture of this relationship because there are individuals that are in only some of the lists, and also individuals that are in none of the lists. These two problems have been solved simultaneously in dual system estimation using the EM algorithm. We extend this approach to four registers (including the population census) to estimate the size of the indigenous Māori population in New Zealand, where the reporting of Māori is not the same in each register and where there is a further missing data problem, with individuals included in one or more registers who did not provide their ethnicity. We consider the implications for estimating the size of the Māori population from administrative data only