Application Of Composite T-Process Regression Models To Functional Data

Process regression models,such as Gaussian process regression model(GPR),have been widely applied to analyze kinds of functional data.Gaussian process re-gression model with its super fitting ability,as well as simple calculation process and other excellent properties,has become the preferred method for scholars to analyze data.Because Gaussian process is not robust for outliers,more and more scholars choose to use more robust methods and processes to fit the data in order to meet the needs of ac-tual accuracy.Heavy tail process is a good choice.Extended t-process is a heavy tailed process.Based on this process,extended t-process regression model(ETPR)is devel-oped,which is more robust.However,GPR model and eTPR model do not consider the feature changes of the data in the local region,so when the data has more complex local feature changes,their estimation effect is not ideal.The composite Gaussian pro-cess model(CGP)constructs a composite of two Gaussian processes,and by adding an additional local term,it can capture the feature changes of the data in the local area to improve the prediction effect.However,CGP model is still Gaussian process in nature,so it is not robust.This paper introduces a composite of two t-processes(CT),where the first one captures the smooth global trend and the second one models local details.The CT has an advantage in the local variability compared to general t-process.Furthermore,a composite T-process regression(CTP)model is developed,based on the composite t-process.It inherits many nice properties as GPR,while it is more robust against outliers than GPR.In addition to robustness,this paper also proves the information consistency of CTP model.Numerical studies including simulation and real data application show that CTP performs well in prediction.