Suppose that the data is modeled as replicated realizations of a pdimensional random vector whose mean µ is a trend of interest and whose covariance matrix Σ is unknown, positive definite. REACT estimators for the trend involve transformation of the data to a new basis, estimating the risks of a class of candidate linear shrinkage estimators, and selecting the candidate estimator with smallest estimated risk. For Gaussian samples and quadratic loss, the maximum risks of REACT estimators

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... in this paper undercut that of the classically efficient sample mean vector. The superefficiency of the proposed estimators relative to the sample mean is most pronounced when the new basis provides an economical description of the vector Σ −1/2 µ, dimension p is not small, and sample size is much larger than p. A case study illustrates how vague prior knowledge may guide choice of a basis that reduces risk substantially.