Parametric empirical Bayes model selection---some theory, methods and simulation
Nitai D. Mukhopadhyay, Jayanta K. Ghosh · Lecture notes-monograph series · 2003
For nested models within the PEB framework of george and Foster (Biometrika,2000), we study the performance of AIC, BIC and several relatively new PEB rules under 0-1 and prediction loss, through asymptotics and simulation.By way of optimality we introduce a new notion of consistency for 0-1 loss and an oracle or lower bound for prediction loss.The BIC does badly , AIC does well for the prediction problem with least squares estimates.The structure and performance of PEB rules depend on the loss function.Properly chosen they rend to outperform other rules.The data consist of independent r.v's Y^ , i = 1, 2, ,p, j = 1, 2, , r.There are p models M ς , 1 < q < p. Hardly any change occurs if q = 0 is also allowed.Under M ς ,