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Functional data analysis has been a growing field of study in recent decades,and one fundamental task in functional data analysis is estimating the samplelocation. A notion called statistical depth has been extended from multivariatedata to functional data, and it can provide a center-outward order for eachobservation within a sample of functional curves. Making use of this intuitivenature of depth methods, a depth-based trimmed mean where curves with lowerdepth values are excluded can be used as a robust location estimator for thesample. In this project, we first introduced several state-of-the-art depthapproaches for functional data. These depths were half region depth, functionalmajority depth, band depth, modified band depth and functional spatial depth.Then we described a robust location estimator based on functional depth, andstudied performances of these estimators based on different functional depthapproaches via simulation tests. Finally, the test results showed thatestimators based on functional spatial depth and modified band depth exhibitedsuperior performances.

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