ABSTRACT
This chapter discusses the posterior mean. Data has frequently been analyzed as if, to an adequate approximation, errors are normally, identically, and independently distributed. Most robust estimators can be characterized by their weighting patterns, although different criteria have been used in choosing the weights. In L-estimators, the weight given to an observation depends on the percentage point it takes in the ordered sample. George P. Box has argued that when a standard procedure is inadequate, it is the model, not the estimation procedure that requires modification. In dealing with the “bad value” problem, a direct Bayesian Robust analysis with a single contaminated model leads to weighting patterns very similar to those of M-estimators which are claimed by their proponents to work well in practice. This verifies the suggestion that if an appropriate model is employed, appropriate estimates will be obtained using standard estimation methods.
