A local depth measure for general data
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We herein introduce a general local depth measure for data in a Banach space, based on the use of one-dimensional projections. Theoretical properties of the local depth measure are studied, as well as, strong consistency results of the local depth measure 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.
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