Monte Carlo Simulations on robustness of functional location estimator based on several functional depth

Functional data analysis has been a growing field of study in recent decades, and one fundamental task in functional data analysis is estimating the sample location. A notion called statistical depth has been extended from multivariate data to functional data, and it can provide a center-outward order for each observation within a sample of functional curves. Making use of this intuitive nature of depth methods, a depth-based trimmed mean where curves with lower depth values are excluded can be used as a robust location estimator for the sample. In this project, we first introduced several state-of-the-art depth approaches for functional data. These depths were half region depth, functional majority depth, band depth, modified band depth and functional spatial depth. Then we described a robust location estimator based on functional depth, and studied performances of these estimators based on different functional depth approaches via simulation tests. Finally, the test results showed that estimators based on functional spatial depth and modified band depth exhibited superior performances.