Related papers: Quantile tomography: using quantiles with multivar…
A new multivariate concept of quantile, based on a directional version of Koenker and Bassett's traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version,…
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…
The concept of depth represents methods to measure how deep an arbitrary point is positioned in a dataset and can be seen as the opposite of outlyingness. It has proved very useful and a wide range of methods have been developed based on…
We present canonical quantiles and depths for directional data following a distribution which is elliptically symmetric about a direction $\mu$ on the sphere $\mathcal{S}^{d-1}$. Our approach extends the concept of Ley et al. [1], which…
In the field of quantitative imaging, the image information at a pixel or voxel in an underlying domain entails crucial information about the imaged matter. This is particularly important in medical imaging applications, such as…
This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving…
Empirical quantiles for finitely distributed univariate random variables can be obtained by solving a certain linear program. It is shown in this short note that multivariate empirical quantiles can be obtained in a very similar way by…
Despite the renewed interest in the Newey and Powell (1987) concept of expectiles in fields such as econometrics, risk management, and extreme value theory, expectile regression---or, more generally, M-quantile regression---unfortunately…
Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…
Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed…
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…
This work studies the estimation of many statistical quantiles under differential privacy. More precisely, given a distribution and access to i.i.d. samples from it, we study the estimation of the inverse of its cumulative distribution…
Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
Quantile regression is used to study effects of covariates on a particular quantile of the data distribution. Here we are interested in the question whether a covariate has any effect on the entire data distribution, i.e., on any of the…
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 develop an approach to risk classification based on quantile contours and allometric modelling of multivariate anthropometric measurements. We propose the definition of allometric direction tangent to the directional quantile envelope,…
During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and…
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…