Functional, randomized and smoothed multivariate quantile regions

JOURNAL OF MULTIVARIATE ANALYSIS

卷:186

Article

Faugeras, Olivier P.¹  Rueschendorf, Ludger² 

[1] Univ Toulouse 1 Capitole, Toulouse Sch Econ, 1 Esplanade Univ, F-31080 Toulouse 6, France

[2] Univ Freiburg, Math Inst, Zermelostr 1, D-79104 Freiburg, Germany

关键词: Copula;    Depth area;    Mass transportation;    Vector quantiles;   

DOI  :  10.1016/j.jmva.2021.104802

来源: Elsevier

【 摘 要 】

The mass transportation approach to multivariate quantiles in Chernozhukov et al. (2017) was modified in Faugeras and Ruschendorf (2017) by a two steps procedure. In the first step, a mass transportation problem from a spherical reference measure to the copula is solved and combined in the second step with a marginal quantile transformation in the sample space. Also, generalized quantiles given by suitable Markov morphisms are introduced there. In the present paper, this approach is further extended by a functional approach in terms of membership functions, and by the introduction of randomized quantile regions. In addition, in the case of continuous marginals, a smoothed version of the empirical quantile regions is obtained by smoothing the empirical copula. All three extended approaches give empirical quantile ares of exact level and improved stability. The resulting depth areas give a valid representation of the central quantile areas of a multivariate distribution and provide a valuable tool for their analysis. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

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