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Depth in Infinite-dimensional Spaces

  • Stanislav Nagy
Conference paper
  • 133 Downloads
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

Depth is a statistical tool that aims to introduce sensible data-dependent ordering of points in multivariate / function spaces. In theory, this should allow construction of statistical procedures based on ranks, orderings, or quantiles for multi-dimensional data. Some of the natural properties a depth should satisfy in finite-dimensional spaces however lose tractability and appeal as the dimension grows. We introduce the depth in finite-dimensional spaces, and outline particular difficulties one faces when attempting to generalize depths to the situation of functional, or other infinite-dimensional data.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Stanislav Nagy
    • 1
  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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