Trimmed means for functional data

Abstract

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.