FIXED VERSUS RANDOM SAMPLING OF CERTAIN CONTINUOUS PARAMETER PROCESSES
- 1 March 1980
- journal article
- Published by Wiley in Australian Journal of Statistics
- Vol. 22 (1) , 40-49
- https://doi.org/10.1111/j.1467-842x.1980.tb01152.x
Abstract
Summary: Let {Z(t)} be a stochastic point process. When {Z(t)} is Poisson and it is desired to estimate the intensity A, it is shown that the optimal (in terms of Fisher information) discrete sampling scheme is to sample {Z(t)} at predetermined fixed time points. On the other hand, when {Z(t)} is a pure birth process and a maximum likelihood estimator of the birth rate is desired, it is sometimes better to sample at random time points, according to a renewal process. An application of these ideas is given in the estimation of bacterial density in a liquid, by the method of dilutions.Keywords
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