Markov morphisms: a combined copula and mass transportation approach to multivariate quantiles

Olivier Paul Faugeras, and Ludger Rüschendorf. "Markov morphisms: a combined copula and mass transportation approach to multivariate quantiles." Mathematica Applicanda 45.1 (2017): null. <http://eudml.org/doc/293455>.

@article{OlivierPaulFaugeras2017,
abstract = {Our purpose is both conceptual and practical. On the one hand, we discuss the question which properties are basic ingredients of a general conceptual notion of a multivariate quantile. We propose and argue that the object “quantile” should be defined as a Markov morphism which carries over similar algebraic, ordering and topological properties as known for quantile functions on the real line. On the other hand, we also propose a practical quantile Markov morphism which combines a copula standardization and the recent optimal mass transportation method of Chernozhukov et al. (2015). Its empirical counterpart has the advantages of being a bandwidth-free, monotone invariant, a.s. consistent transformation. The proposed the approach gives a general and unified framework to quantiles and their corresponding depth areas, for both a continuous or a discrete multivariate distribution.},
author = {Olivier Paul Faugeras, Ludger Rüschendorf},
journal = {Mathematica Applicanda},
keywords = {Statistical depth; vector quantiles; Markov morphism; copula; Mass transportation},
language = {eng},
number = {1},
pages = {null},
title = {Markov morphisms: a combined copula and mass transportation approach to multivariate quantiles},
url = {http://eudml.org/doc/293455},
volume = {45},
year = {2017},
}

TY - JOUR
AU - Olivier Paul Faugeras
AU - Ludger Rüschendorf
TI - Markov morphisms: a combined copula and mass transportation approach to multivariate quantiles
JO - Mathematica Applicanda
PY - 2017
VL - 45
IS - 1
SP - null
AB - Our purpose is both conceptual and practical. On the one hand, we discuss the question which properties are basic ingredients of a general conceptual notion of a multivariate quantile. We propose and argue that the object “quantile” should be defined as a Markov morphism which carries over similar algebraic, ordering and topological properties as known for quantile functions on the real line. On the other hand, we also propose a practical quantile Markov morphism which combines a copula standardization and the recent optimal mass transportation method of Chernozhukov et al. (2015). Its empirical counterpart has the advantages of being a bandwidth-free, monotone invariant, a.s. consistent transformation. The proposed the approach gives a general and unified framework to quantiles and their corresponding depth areas, for both a continuous or a discrete multivariate distribution.
LA - eng
KW - Statistical depth; vector quantiles; Markov morphism; copula; Mass transportation
UR - http://eudml.org/doc/293455
ER -