On similarity of the sample projection depth contours and its application

Yefang Yuan, Xiaohui Liu, Yuting Chen, Yuxin Dong and Yuzi Liu

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 7, 1919-1935

Abstract: In this paper, we investigate the similarity property of the sample projection depth contours. It turns out that parts of the projection depth contours are of the same shape but with different sizes, behaving similarly to contours induced from the Mahalanobis depth. The major application of this investigation is that we may exploit the idea behind the similarity property to extend both the halfspace depth and zonoid depth to versions that do not vanish outside the convex hull of the data cloud, so that we can overcome the so-called ‘outside problem’ of these two depths.

Date: 2022
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DOI: 10.1080/03610926.2020.1802651

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