The zonoid region parameter depth Articles uri icon

publication date

  • December 2022

International Standard Serial Number (ISSN)

  • 0932-5026

Electronic International Standard Serial Number (EISSN)

  • 1613-9798

abstract

  • A new concept of depth for central regions is introduced. The proposed depth notion assesses how well an interval fits a given univariate distribution as its zonoid region of level 1/2, and it is extended to the multivariate setting by means of a projection argument. Since central regions capture information about location, scatter, and dependency among several variables, the new depth evaluated on an empirical zonoid region quantifies the degree of similarity (in terms of the features captured by central regions) of the corresponding sample with respect to some reference distribution. Applications to statistical process control and the joint monitoring of multivariate and interval-valued data in terms of location and scale are presented.

subjects

  • Statistics

keywords

  • data dept; parameter depth; random interval; zonoid depth