  Gaussian process regression (GPR) model is well-known to be susceptible to
outliers. Robust process regression models based on t-process or other
heavy-tailed processes have been developed to address the problem. However, due
to the nature of the current definition for heavy-tailed processes, the unknown
process regression function and the random errors are always defined jointly
and thus dependently. This definition, mainly owing to the dependence
assumption involved, is not justified in many practical problems and thus
limits the application of those robust approaches. It also results in a
limitation of the theory of robust analysis. In this paper, we propose a new
robust process regression model enabling independent random errors. An
efficient estimation procedure is developed. Statistical properties, such as
unbiasness and information consistency, are provided. Numerical studies show
that the proposed method is robust against outliers and has a better
performance in prediction compared with the existing models. We illustrate that
the estimated random-effects are useful in detecting outlying curves.
