Linear statistics in change-point estimation and their asymptotic behaviour. (English) Zbl 0879.62019

Summary: The limiting behaviour of Bayes procedures in the asymptotic setting of the change-point estimation problem is studied. It is shown that the distribution of the difference between the Bayes estimator and the parameter converges to the distribution of a fairly complicated random variable. A class of linear statistics is introduced, and the form of the Bayes estimator within this class is deduced. The asymptotic properties of this linear estimator are investigated in two different settings for the prior distribution.


62F12 Asymptotic properties of parametric estimators
62F15 Bayesian inference
62E20 Asymptotic distribution theory in statistics
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