  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.
