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Bayesian inference based on robust priors and MML estimators. I: Symmetric location-scale distributions. (English) Zbl 0897.62027

Summary: Motivated by the attractive features of robust priors and the maximum likelihood estimators, we develop Bayesian estimators for the location parameter of a family which represents a very wide class of symmetric location-scale distributions ranging from Cauchy to normal distributions. We show that the new estimators are clearly superior to those obtained earlier by other authors. The proposed method can also be extended to asymmetric location-scale distributions. That will form Part II of this work.

MSC:

62F15 Bayesian inference
62F10 Point estimation
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