Note on the applicability of the James-Stein Estimator in regional hydrologic studies

The applicability of the James-Stein estimator in regional hydrologic studies which entail the estimation of an N-dimensional location parameter is discussed. Regional studies are frequently characterized by relatively short, generally correlated, samples drawn from nonsymmetric and bounded, i.e., nonnormal, populations. By means of computer simulation studies the James-Stein estimator, subject to the Lindley modification and adoption of the positive part rule suggested by Efron and Morris and conditioned on the assumption of independence, was shown to be robust in the case of the hydrologically plausible distribution considered here, namely, Weibull distributions with coefficient of skewness ranging from 0 to 10. However, in contrast to traditional methods of regionalization the effect of cross correlation is a diminishment of the relative risk advantage of the James-Stein estimator, even in the best case of normal variables : this is discussed and illustrated.