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B0668
Title: Perspectives on multivariate depth and quantile functions Authors:  Robert Serfling - University of Texas at Dallas (United States) [presenting]
Abstract: Various properties are desirable for multivariate depth functions, such as invariance under selected transformations, robustness, and computational ease, among others. These play a central role in choosing a particular depth function. Since such criteria trade off against each other, one must prioritize, based on the application context and the statistical inference goals. Similarly, there are desirable equivariance and other properties for the quantile and rank functions that are closely related to a given depth function. However, in the case of rank functions, for example, the relevant priorities arise from quite different conceptual orientations and may differ from those for the depth functions, even though the corresponding depth and rank functions are equivalent in some sense. It is important, therefore, to delineate precisely the correspondence between multivariate depth and rank functions and on this basis to revisit and either reaffirm or update standing priorities on desired criteria for such functions. One seeks both technical and conceptual consistency between, say, the priorities for depth function properties and those for rank function properties. Some relevant foundation and perspective on these and related issues will be provided.