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Let X=(X₁,..., Xₙ) be a sample from a distribution with density f(x;θ), θ ∈ Θ ⊂ ℝ. In this article the Bayesian estimation of the parameter θ is considered. We examine whether the Bayes estimators of θ are pointwise ordered when the prior distributions are partially ordered. Various cases of loss function are studied. A lower bound for the survival function of the normal distribution is obtained.
Piotr Bolesław Nowak. "Monotonicity of Bayes estimators." Applicationes Mathematicae 40.4 (2013): 393-404. <http://eudml.org/doc/279904>.
@article{PiotrBolesławNowak2013, abstract = {Let X=(X₁,..., Xₙ) be a sample from a distribution with density f(x;θ), θ ∈ Θ ⊂ ℝ. In this article the Bayesian estimation of the parameter θ is considered. We examine whether the Bayes estimators of θ are pointwise ordered when the prior distributions are partially ordered. Various cases of loss function are studied. A lower bound for the survival function of the normal distribution is obtained.}, author = {Piotr Bolesław Nowak}, journal = {Applicationes Mathematicae}, keywords = {maximum a posteriori estimation; exponential family; weighted distribution; stochastic ordering; pointwise domination; total positivity; unimodality; squared error loss; weighted squared error loss; uniform loss function; asymmetric loss function}, language = {eng}, number = {4}, pages = {393-404}, title = {Monotonicity of Bayes estimators}, url = {http://eudml.org/doc/279904}, volume = {40}, year = {2013}, }
TY - JOUR AU - Piotr Bolesław Nowak TI - Monotonicity of Bayes estimators JO - Applicationes Mathematicae PY - 2013 VL - 40 IS - 4 SP - 393 EP - 404 AB - Let X=(X₁,..., Xₙ) be a sample from a distribution with density f(x;θ), θ ∈ Θ ⊂ ℝ. In this article the Bayesian estimation of the parameter θ is considered. We examine whether the Bayes estimators of θ are pointwise ordered when the prior distributions are partially ordered. Various cases of loss function are studied. A lower bound for the survival function of the normal distribution is obtained. LA - eng KW - maximum a posteriori estimation; exponential family; weighted distribution; stochastic ordering; pointwise domination; total positivity; unimodality; squared error loss; weighted squared error loss; uniform loss function; asymmetric loss function UR - http://eudml.org/doc/279904 ER -