BAYESIAN-INFERENCE BASED ON ROBUST PRIORS AND MML ESTIMATORS .1. SYMMETRICAL LOCATION-SCALE DISTRIBUTIONS

Motivated by the attractive features of robust priors and the MML esti mators, 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 th at the new estimators are clearly superior to those obtained earlier b y other authors. The proposed method can also be extended to asymmetri c location-scale distributions. That will form Part II of this work.