The proven optimality properties of empirical Bayes estimators and their documented successful performance in practice have made them popular. Although many statisticians have used these estimators since the landmark paper of James and Stein (1961), relatively few have proposed techniques for protecting them from the effects of outlying observations or outlying parameters. One notable series of studies in protection against outlying parameters was conducted by Efron and Morris (1971, 1972, 1975). In the fully Bayesian case, a general discussion on robust procedures can be found in Berger (1984, 1985). Here we implement and evaluate a different approach for outlier protection in a random‐effects model which is based on appropriate specification of the prior distribution. When unusual parameters are present, we estimate the prior as a step function, as suggested by Laird and Louis (1987). This procedure is evaluated empirically, using a number of simulated data sets to compare the effects of the step‐function prior with those of the normal and Laplace priors on the prediction of small‐area proportions. Copyright

Empirical Bayes estimation, Laplace prior, logistic regression, nonparametric maximum‐likelihood estimation, normal prior, outliers, Primary 62D05, random‐effects models, secondary 62F15., small‐area estimation., step‐function prior
dx.doi.org/10.2307/3315598
Canadian Journal of Statistics
Sprott School of Business

Farrell, P, Macgibbon, B. (Brenda), & Tomberlin, T.J. (1994). Protection against outliers in empirical bayes estimation. Canadian Journal of Statistics, 22(3), 365–376. doi:10.2307/3315598