The Duality of Diagnostic Checking and Robustification in Model Building: Some Considerations and Examples

摘要

Consideration is given to the means by which appropriate diagnostic checking functions of the data can be developed to guard against feared model discrepancies. A formal basis for the selection of a function is given for situations where the feared inadequacy can be characterized by a discrepancy parameter beta which takes a (possible inappropriate) value of beta sub zero in the model. The relationship of this checking function with the posterior distribution obtained from an elaborated ('robustified') model which allows for the discrepancy parameter to be estimated is discussed. The nature of the diagnostic check is briefly described for problems relating to transformation of the dependent variable and to serial correlation; while a more thorough investigation of the checking function is given for problems relating to outlying observations and to transformation of predictor variables. Several examples are given to illustrate these ideas.