# Robust functional ANOVA model with t-process

## TL;DR

This paper introduces a robust functional ANOVA model using t-processes to improve estimation and prediction in the presence of outliers, with proven statistical properties and demonstrated effectiveness through simulations and real data.

## Contribution

It develops a novel robust estimation method for functional ANOVA models utilizing t-processes, enhancing robustness and prediction accuracy.

## Key findings

- Method performs well in simulations
- Effective in real data applications
- Ensures robustness and consistency

## Abstract

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.