A general robust t-process regression model

The 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 current definitions of heavy-tailed processes, the unknown process regression function and the random errors are always defined jointly. This definition, mainly owing to mix-up of the regression function modeling and the distribution of the random errors, is not justified in many practical problems and thus limits the application of those robust approaches. It also results in a limitation of the statistical properties and robust analysis. A general robust process regression model is proposed by separating the nonparametric regression model from the distribution assumption of the random error. An efficient estimation procedure is developed. It shows that the estimated random-effects are useful in detecting outlying curves. Statistical properties, such as unbiasedness and information consistency, are provided. Numerical studies show that the proposed method is robust against outliers and outlying curves, and has a better performance in prediction compared with the existing models.