Completeness and unbiased estimation in sequential multinomial sampling

A sufficient but not necessary condition for completeness is given in the case of sequential sampling from multinomial populations. Uniform minimum variance unbiased estimators which follow from completeness and conditional distributions are given for some cases to demonstrate the procedure. An example where sequential sampling was actually used with food selection by leaf cutter ants is also given and discussed. While practical differences between unbiased and biased estimators may be insignificant for individual samples, unbiased estimators may outperform maximum likelihood estimators for multiple sequential samples.