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Robust estimation approaches are of fundamental importance for statistical modelling. To reduce susceptibility to outliers, we propose a robust estimation procedure with t-process under functional ANOVA model. Besides common mean structure of the studied subjects, their personal characters are also informative, especially for prediction. We develop a prediction method to predict the individual effect. Statistical properties, such as robustness and information consistency, are studied. Numerical studies including simulation and real data examples show that the proposed method performs well.
In observational clinic registries, time to treatment is often of interest, but treatment can be given at any time during follow-up and there is no structure or intervention to ensure regular clinic visits for data collection. To address these challe
We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student $t$-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting conditional
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 gi
Robust estimation and variable selection procedure are developed for the extended t-process regression model with functional data. Statistical properties such as consistency of estimators and predictions are obtained. Numerical studies show that the proposed method performs well.
Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in the prese