We consider two approaches to robust estimation for the Box-Cox power transfonnation "model. one approach maximizes weighted, modified likelihoods. A second approach bounds the self-standardized gross-error sensitivity, a measure of the potential influence of outliers pIoneered by KrasKer and Welsch (JASA, 1982). Among our primary concerns is the performance of these estimators on actual data. ln examples that we study, there seem to be only minor dIfferences beuween these three estlmators, but

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... they behave rather differently than the maximum likelihood estimator or eSLimators that bound only the lTIfluence of the residuals. Confidence limits for the transfonnatlon parameter can be obtained by using a large-sample nonnal approximation or by modified likelihood-ratIo testIng. These examples show that model selection, determinatIon of the transfonnation parameter, and outlier identification are fundamentally interconnected. Carroll (1982) shows that it can be particularly useful in designed experiments which have large outliers; see this last paper for computational conventions.