Estimation of Parameters of Zero-One Processes by Interval Sampling: An Adaptive Strategy

We have considered before the problem of estimating the parameters giving the mean time in each stage, for a two-stage Poisson process, when sampling was permitted only at equal intervals. It was impossible to get good results unless the intervals were small. We now propose an adaptive strategy in which the interval is successively halved until a suitable stage is reached; then all samples can be combined to give estimates. The strategy is examined by Monte Carlo methods, and it is shown to give a considerable improvement over the one-stage method. Figures are given to illustrate the results; they can be used also to improve estimates and give confidence intervals. We propose a technique to give an approximate confidence ellipse for the two parameters, which works well for the ranges considered.