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 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 are enough to obtain an asymptotically unbiased population size estimate. However, the assumption of sample independence may be unrealistic, especially when the samples are derived from administrative sources. The assumption of sample independence can be relaxed when using three or more samples, 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 utilizing older samples, using the so-called expectation maximization 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, leading to reasonably accurate nowcast estimates.