Local depth |
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| Authors: | Claudio AgostinelliMario Romanazzi |
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| Institution: | a Dipartimento di Statistica and Scuola Superiore di Economia, Università Ca'' Foscari di Venezia, Fondamenta S. Giobbe, Cannaregio 873, 30121 Venezia, Italy
b Dipartimento di Statistica, Universitá Ca’ Foscari di Venezia, Fondamenta S. Giobbe, Cannaregio 873, 30121 Venezia, Italy |
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| Abstract: | Local depth is a generalization of ordinary depth able to reveal local features of the probability distribution. Liu's simplicial depth is primarily used, but results for Tukey's halfspace depth are also derived. It is shown that the maximizers of local depth can help to detect the mode(s) of a probability distribution. This work is devoted to the univariate case, but the main definitions are stated in the general multivariate case. Theoretical results and applications are illustrated with several examples. |
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| Keywords: | Data depth Halfspace depth Multimodal distribution Simplicial depth |
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