  Gaussian process regression (GPR) model has been widely used to fit data when
the regression function is unknown and its nice properties have been well
established. In this article, we introduce an extended t-process regression
(eTPR) model, a nonlinear model which allows a robust best linear unbiased
predictor (BLUP). Owing to its succinct construction, it inherits many
attractive properties from the GPR model, such as having closed forms of
marginal and predictive distributions to give an explicit form for robust
procedures, and easy to cope with large dimensional covariates with an
efficient implementation. Properties of the robustness are studied. Simulation
studies and real data applications show that the eTPR model gives a robust fit
in the presence of outliers in both input and output spaces and has a good
performance in prediction, compared with other existed methods.
