A local depth measure for general data

TL;DR

This paper introduces the Integrated Dual Local Depth, a new local depth measure for data in Banach spaces using projections, with theoretical properties, consistency results, and applications to multivariate functional data analysis.

Contribution

The paper proposes a novel local depth measure for Banach space data based on projections, with theoretical analysis and practical applications to multivariate functional data.

Findings

Strong consistency results for the local depth and regions.

Effective application to multivariate functional data analysis.

Promising results in classification tasks.

Abstract

We introduce the Integrated Dual Local Depth which is a local depth measure for data in a Banach space based on the use of one-dimensional projections. The properties of a depth measure are analyzed under this setting and a proper definition of local symmetry is given. Moreover, strong consistency results for the local depth and also for the local depth regions are attained. Finally, applications to descriptive data analysis and classification are analyzed, making the special focus on multivariate functional data, where we obtain very promising results.