@bullet Transformations in Regression: a Robust Analysis

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 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. lDepartment of Statistics, UnIversity of North Carolina aL Chapel Hill. bUpporred by the AIr Force Office of Scientific Research Contract No. AFOSR F49620 82 C 0009. 2Department of Statistics, UnIversity of North Carolina aL Chapel Hill. supporLed by the National SCIence FoundatlOn Grant MCS 8l0074~.