On efficient stopping times. (English) Zbl 0568.62075
The author considers the problem of sequential estimation for a stochastic process where the sufficient statistics form a process of the exponential class. A sequential plan (\(\tau\),f,h) consists of a stopping time \(\tau\), a real function h of the unknown k-dimensional parameter and an unbiased estimator f of h. A sequential plan is called efficient if it yields equality in the Cramér-Rao-inequality for all parameters in some k-dimensional interval.
In this paper, the author characterizes all stopping times for which there exist f and h as above such that (\(\tau\),f,h) is efficient. Some examples are given which illustrate this characterization.
In this paper, the author characterizes all stopping times for which there exist f and h as above such that (\(\tau\),f,h) is efficient. Some examples are given which illustrate this characterization.
Reviewer: A.Irle
Keywords:
stationary independent increments; Markov stopping time; efficiency; sufficient statistics; process of the exponential class; sequential plan; unbiased estimator; Cramér-Rao-inequalityReferences:
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