Robust prediction limits based on M-estimators

We discuss a robust solution to the problem of prediction. Extending Barndorff-Nielsen and Cox [1996. Prediction and asymptotics. Bernoulli 2, 319–340] and Vidoni [1998. A note on modified estimative prediction limits and distributions. Biometrika 85, 949–953], we propose improved prediction limits based on M-estimators. To compute them, the expressions of the bias and variance of an M-estimator are required. In view of this, a general asymptotic approximation for the bias of an M-estimator is derived. Moreover, by means of comparative studies in the context of affine transformation models, we show that the proposed robust procedure for prediction can be successfully used in a parametric setting.