相关论文: Center-Outward Distribution Functions, Quantiles, …
All multivariate extensions of the univariate theory of risk measurement run into the same fundamental problem of the absence, in dimension d > 1, of a canonical ordering of Rd. Based on measure transportation ideas, several attempts have…
Extending to dimension 2 and higher the dual univariate concepts of ranks and quantiles has remained an open problem for more than half a century. Based on measure transportation results, a solution has been proposed recently under the name…
Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century. None of the many solutions…
In this paper we study multivariate ranks and quantiles, defined using the theory of optimal transport, and build on the work of Chernozhukov et al.(2017) and Hallin et al.(2021). We study the characterization, computation and properties of…
For a probability P in $R^d$ its center outward distribution function $F_{\pm}$, introduced in Chernozhukov et al. (2017) and Hallin et al. (2021), is a new and successful concept of multivariate distribution function based on mass…
We propose center-outward superquantile and expected shortfall functions, with applications to multivariate risk measurements, extending the standard notion of value at risk and conditional value at risk from the real line to…
We provide sufficient conditions under which the center-outward distribution and quantile functions introduced in Chernozhukov et al.~(2017) and Hallin~(2017) are homeomorphisms, thereby extending a recent result by Figalli \cite{Fi2}. Our…
We propose new concepts of statistical depth, multivariate quantiles, ranks and signs, based on canonical transportation maps between a distribution of interest on $R^d$ and a reference distribution on the $d$-dimensional unit ball. The new…
To generalize the notion of distribution function to dimension $d\geq 2$, in the recent papers it was proposed a concept of center-outward distribution function based on optimal transportation ideas, and the inferential properties of the…
Quantiles are a fundamental concept in probability and theoretical statistics and a daily tool in their applications. While the univariate concept of quantiles is quite clear and well understood, its multivariate extension is more…
Increased attention has been given recently to the statistical analysis of variables with values on nonlinear manifolds. A natural but nontrivial problem in that context is the definition of quantile concepts. We are proposing a solution…
Rank correlations have found many innovative applications in the last decade. In particular, suitable rank correlations have been used for consistent tests of independence between pairs of random variables. Using ranks is especially…
Stochastic dominance (SD) provides a quantile-based partial ordering of random variables and has broad applications. Its extension to multivariate settings, however, is challenging due to the lack of a canonical ordering in $\mathbb{R}^d$…
This paper proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile…
Due to the lack of a canonical ordering in ${\mathbb R}^d$ for $d>1$, defining multivariate generalizations of the classical univariate ranks has been a long-standing open problem in statistics. Optimal transport has been shown to offer a…
In this paper, we propose a general framework for distribution-free nonparametric testing in multi-dimensions, based on a notion of multivariate ranks defined using the theory of measure transportation. Unlike other existing proposals in…
A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…
Based on the novel concept of multivariate center-outward quantiles introduced recently in Chernozhukov et al. (2017) and Hallin et al. (2021), we are considering the problem of nonparametric multiple-output quantile regression. Our…
The pseudo-Gaussian portmanteau tests of Chitturi, Hosking, and Li and McLeod for VARMA models are revisited from a Le Cam perspective, providing a precise and more rigorous description of the asymptotic behavior of the multivariate…
This paper reviews recent advancements in the application of optimal transport (OT) to multivariate distribution-free nonparametric testing. Inspired by classical rank-based methods, such as Wilcoxon's rank-sum and signed-rank tests, we…