Two semi parametric empirical Bayes estimators

Parametric empirical Bayes PEB may perform poorly when the assumed prior distribution is seriously invalid Nonparametric empirical Bayes NEB is more robust since it imposes no restric tion on the prior But compared with the PEB the NEB may be ine cient for small to medium samples due to the large variation and under dispersion of the NPMLE of the prior Using Monte Carlo simulations we compare two semi parametric estimators designed to strike a trade o be tween e ciency and robustness a weighted average of the PEB and NEB and a kernel smoother of the NPMLE Both estimators depend on likelihood cross validation for choosing appropriate parameters For illustration we reanalyze two data sets from Efron and Morris