Standard Article


Statistical Theory and Methods

  1. Robert Serfling

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vnn080

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Serfling, R. 2013. Depth. Encyclopedia of Environmetrics. 2.

Author Information

  1. University of Texas at Dallas, TX, US

Publication History

  1. Published Online: 15 JAN 2013


Depth functions represent a recently emerging powerful methodology in nonparametric multivariate inference. They provide multivariate notions of order statistics and generate quantile contours, outlyingness functions, and sign and rank functions. There are wide possibilities for constructing such functions, but these narrow considerably when criteria such as affine equivariance or invariance, computational ease, asymptotic behavior, and robustness are applied. We review basic definitions, leading examples, key properties, and selected applications.


  • multivariate;
  • nonparametric;
  • depth functions;
  • quantiles;
  • outlyingness functions;
  • signs and ranks