FIXED VERSUS RANDOM SAMPLING OF CERTAIN CONTINUOUS PARAMETER PROCESSES
作者:
Philip McDunnough,
David B. Wolfson,
期刊:
Australian Journal of Statistics
(WILEY Available online 1980)
卷期:
Volume 22,
issue 1
页码: 40-49
ISSN:0004-9581
年代: 1980
DOI:10.1111/j.1467-842X.1980.tb01152.x
出版商: Blackwell Publishing Ltd
关键词: Birth process;Discrete sampling;Poisson process;Fisher information
数据来源: WILEY
摘要:
SummaryLet {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.
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