A local depth measure for general data

Abstract

We introduce a local depth measure for data in a Banach space, based on the use of one-dimensional projections. Its theoretical properties are studied, as well as strong consistency results for it and also of the local depth regions. In addition, we propose a clustering procedure based on local depths. Applications of the clustering procedure are illustrated on some artificial and real data sets for multivariate, functional, and multifunctional data, obtaining very promising results.