  Robust estimation approaches are of fundamental importance for statistical
modelling. To reduce susceptibility to outliers, we propose a robust estimation
procedure with t-process under functional ANOVA model. Besides common mean
structure of the studied subjects, their personal characters are also
informative, especially for prediction. We develop a prediction method to
predict the individual effect. Statistical properties, such as robustness and
information consistency, are studied. Numerical studies including simulation
and real data examples show that the proposed method performs well.
