Aligning of Estimates: An Alternative to Empirical Bayes Methods

Summary The data that are used in constructing empirical Bayes estimates can properly be regarded as arising in a two‐stage sampling scheme. In this setting it is possible to modify the conventional parameter estimates so that a reduction in expected squared error is effected. In the empirical Bayes approach this is done through the use of Bayes's theorem. The alternative approach proposed in this paper specifies a class of modified estimates and then seeks to identify that member of the class which yields the minimum squared error. One advantage of this approach relative to the empirical Bayes approach is that certain problems involving multiple parameters are easily overcome. Further, it permits the use of relatively efficient methods of non‐parametric estimation, such as those based on quantiles or ranks; this has not been achieved by empirical Bayes methods.