A new statistical depth function with applications to multimodal data

Abstract

We propose a new statistical depth function based on interpoint distances, which has the distinct property of respecting multimodality in data configurations. This property proves to be especially relevant to many inference problems including confidence region construction, classification, tests for equality of populations, p-value computation, etc. With specification of an appropriate interpoint distance, our depth function also applies to infinite-dimensional data. A number of examples are used to illustrate the diverse applicability of our proposed depth function in different problem settings, where the conventional centre-outward ordering depth functions are found to be inadequate.

Keywords:

• centre-outward ordering
• data depth
• interpoint distance
• multimodality

2000 MSC code:

• 62G99

Acknowledgements

W.S.L. was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7128/02P). S.M.S.L. was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7029/04P).