Two point priors and Γ-minimax estimating in families of uniform distributions
Copyright policy )Two point priors and Γ-minimax estimating in families of uniform distributions
It is shown that when a parameter lying in a sufficiently small interval is to be estimated in a family of uniform distributions, a two point prior is least favourable under squared error loss. The unique Bayes estimator with respect to this prior is minimax. The \(\Gamma\)-minimax estimator is derived for sets \(\Gamma\) of priors consisting of all priors that give fixed probabilities to two specified subintervals of the parameter space if a two point prior is least favourable in \(\Gamma\).
Statistical decision theory, Minimax procedures in statistical decision theory, Bayesian inference, Point estimation, uniform distributions, Bayesian problems; characterization of Bayes procedures, squared error loss, gamma minimax estimator, two point prior, least favourable
Statistical decision theory, Minimax procedures in statistical decision theory, Bayesian inference, Point estimation, uniform distributions, Bayesian problems; characterization of Bayes procedures, squared error loss, gamma minimax estimator, two point prior, least favourable
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