Trimmed means for functional data

In practice, the use of functional data is often preferable to that of large finitedimensional vectors obtained by discrete approximations of functions. In this paper a new concept of data depth is introduced for functional data. The aim is to measure the centrality of a given curve within a group of curves. This concept is used to define ranks and trimmed means for functional data. Some theoretical and practical aspects are discussed and a simulation study is given. The results show a good performance of our method, in terms of efficiency and robustness, when compared with the mean. Finally, a real-data example based on the Nasdaq 100 index is discussed.