Change-Point Analysis as a Multiple Decision Problem
Copyright policy )Change-Point Analysis as a Multiple Decision Problem
Summary: In the classical setting of the change-point estimation problem a positive limit of the minimum Bayes risk for the uniform prior is shown to exist for any loss. Its explicit form and some inequalities are derived for the zero-one loss function. The nature of minimum Bayes risk is shown to be related to the multiple decision problem and to information-type characteristics.
Hellinger affinity, super-additive sequence, uniform prior, Renyi entropy, minimum Bayes risk, Bayesian problems; characterization of Bayes procedures, inequalities, maximum likelihood procedure, Bernoulli distributions, change-point estimation problem, zero-one loss function, error probability, multiple decision problem, Asymptotic properties of parametric estimators
Hellinger affinity, super-additive sequence, uniform prior, Renyi entropy, minimum Bayes risk, Bayesian problems; characterization of Bayes procedures, inequalities, maximum likelihood procedure, Bernoulli distributions, change-point estimation problem, zero-one loss function, error probability, multiple decision problem, Asymptotic properties of parametric estimators
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