  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, which gives 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 BLUP procedures, and easy to cope with
large dimensional covariates with an efficient implementation by slightly
modifying existing BLUP procedures. Properties of the robust BLUP 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 the GPR and locally weighted
scatterplot smoothing (LOESS) methods.
