Nowcasting in triple-system estimation

Multiple systems estimation uses samples that each cover part of a population to obtain a total population size estimate. Ideally, all the available samples are used, but if some samples are available (much) later, one may use only the samples that are available early. Under some regularity conditions, including sample independence, two samples is enough to obtain an asymptotically unbiased population size estimate. However, the assumption of sample independence may be unrealistic, especially when samples are derived from administrative sources. The sample independence assumption can be relaxed when three or more samples are used, which is therefore generally recommended. This may be a problem if the third sample is available much later than the first two samples. Therefore, in this paper we propose a new approach that deals with this issue by utilising older samples, using the so-called expectation maximisation algorithm. This leads to a population size nowcast estimate that is asymptotically unbiased under more relaxed assumptions than the estimate based on two samples. The resulting nowcasting model is applied to the problem of estimating the number of homeless people in The Netherlands, which leads to reasonably accurate nowcast estimates.