Extremal Fits in React Confidence Sets

REACT estimators use ideas from signal processing, model-selection, and shrinkage to achieve much smaller risk in one-way layouts and other linear models than does the classical least squares estimator. The REACT method can generate automatic scatterplot smoothers that compete well on standard data sets with the best fits obtained by other methods. This paper addresses two further questions: Which features in a REACT estimator are not necessarily present in the true mean vector; and which features of the true mean vector might have been smoothed out by the REACT estimator? We answer both questions by constructing extremal members of a confidence set of asymptotic coverage probability α that is centered at the REACT estimator. The methodology is demonstrated on two data-sets from the smoothing literature.