Related papers: Quantiles and Quantile Regression on Riemannian Ma…
Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view…
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…
A Riemannian stochastic representation of model uncertainties in molecular dynamics is proposed. The approach relies on a reduced-order model, the projection basis of which is randomized on a subset of the Stiefel manifold characterized by…
This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for…
Flexible estimation of multiple conditional quantiles is of interest in numerous applications, such as studying the effect of pregnancy-related factors on low and high birth weight. We propose a Bayesian non-parametric method to…
Quantile regression models provide a wide picture of the conditional distributions of the response variable by capturing the effect of the covariates at different quantile levels. In most applications, the parametric form of those…
Quantile regression relates the quantile of the response to a linear predictor. For a discrete response distributions, like the Poission, Binomial and the negative Binomial, this approach is not feasible as the quantile function is not…
I introduce a generic method for inference on entire quantile and regression quantile processes in the presence of a finite number of large and arbitrarily heterogeneous clusters. The method asymptotically controls size by generating…
Quantile is a popular performance measure for a stochastic system to evaluate its variability and risk. To reduce the risk, selecting the actions that minimize the tail quantiles of some loss distributions is typically of interest for…
Quantile regression (QR) is a powerful tool for estimating one or more conditional quantiles of a target variable $\mathrm{Y}$ given explanatory features $\boldsymbol{\mathrm{X}}$. A limitation of QR is that it is only defined for scalar…
This paper is written for a Festschrift in honour of Professor Marc Hallin and it proposes some developments on quantile regression. We connect our investigation to Marc's scientific production and we present some theoretical and…
This paper deals with a linear model of regression on quantiles when the explanatory variable takes values in some functional space and the response is scalar. We propose a spline estimator of the functional coefficient that minimizes a…
We consider parameter inference for linear quantile regression with non-stationary predictors and errors, where the regression parameters are subject to inequality constraints. We show that the constrained quantile coefficient estimators…
This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable…
This paper defines an alternative notion, described as data-based, of geometric quantiles on Hadamard spaces, in contrast to the existing methodology, described as parameter-based. In addition to having the same desirable properties as…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…
This paper defines quantiles, ranks and statistical depths for image data by leveraging ideas from measure transportation. The first step is to embed a distribution of images in a tangent space, with the framework of linear optimal…
We introduce classifiers based on directional quantiles. We derive theoretical results for selecting optimal quantile levels given a direction, and, conversely, an optimal direction given a quantile level. We also show that the…
We develop a model-free theory of general types of parametric regression for iid observations. The theory replaces the parameters of parametric models with statistical functionals, to be called "regression functionals'', defined on large…