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Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider…

Statistics Theory · Mathematics 2009-09-29 Mi-Ok Kim

Quantile regression is a powerful tool capable of offering a richer view of the data as compared to least-squares regression. Quantile regression is typically performed individually on a few quantiles or a grid of quantiles without…

Methodology · Statistics 2026-03-26 Ta-Hsin Li , Nimrod Megiddo

Quantile regression is a technique to estimate conditional quantile curves. It provides a comprehensive picture of a response contingent on explanatory variables. In a flexible modeling framework, a specific form of the conditional quantile…

Statistics Theory · Mathematics 2012-08-31 Vladimir Spokoiny , Weining Wang , Wolfgang Karl Härdle

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…

Methodology · Statistics 2016-08-08 Xiaowen Dai , Shaoyang Li , Maozai Tian

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…

Computation · Statistics 2023-06-05 Aviv A. Rosenberg , Sanketh Vedula , Yaniv Romano , Alex M. Bronstein

The quantile-crossing spectrum is the spectrum of quantile-crossing processes created from a time series by the indicator function that shows whether or not the time series lies above or below a given quantile at a given time. This…

Methodology · Statistics 2026-03-26 Ta-Hsin Li

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…

Data Structures and Algorithms · Computer Science 2014-01-08 Jiyan Yang , Xiangrui Meng , Michael W. Mahoney

Quantile is an important risk measure quantifying the stochastic system random behaviors. This paper studies a pooled quantile estimator, which is the sample quantile of detailed simulation outputs after directly pooling independent sample…

Methodology · Statistics 2019-10-15 Qiong Zhang , Bo Wang , Wei Xie

Quantile Regression (QR) provides a way to approximate a single conditional quantile. To have a more informative description of the conditional distribution, QR can be merged with deep learning techniques to simultaneously estimate multiple…

Machine Learning · Computer Science 2022-02-01 Axel Brando , Joan Gimeno , Jose A. Rodríguez-Serrano , Jordi Vitrià

Quantile estimation is a problem presented in fields such as quality control, hydrology, and economics. There are different techniques to estimate such quantiles. Nevertheless, these techniques use an overall fit of the sample when the…

Quantile regression (QR) is a statistical tool for distribution-free estimation of conditional quantiles of a target variable given explanatory features. QR is limited by the assumption that the target distribution is univariate and defined…

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.…

Databases · Computer Science 2015-08-25 Zixuan Zhuang

While probabilistic forecast verification for categorical forecasts is well established, some of the existing concepts and methods have not found their equivalent for the case of continuous variables. New tools dedicated to the assessment…

Atmospheric and Oceanic Physics · Physics 2015-10-02 Zied Ben Bouallegue , Pierre Pinson , Petra Friederichs

This paper addresses computational challenges in estimating Quantile Regression with Selection (QRS). The estimation of the parameters that model self-selection requires the estimation of the entire quantile process several times. Moreover,…

Econometrics · Economics 2024-02-27 Santiago Pereda-Fernández

Quantile regression is a statistical method for estimating conditional quantiles of a response variable. In addition, for mean estimation, it is well known that quantile regression is more robust to outliers than $l_2$-based methods. By…

Methodology · Statistics 2021-08-18 Steven Siwei Ye , Oscar Hernan Madrid Padilla

In this paper, we consider a generic scheme that allows building weighted versions of various quantile estimators, such as traditional quantile estimators based on linear interpolation of two order statistics, the Harrell-Davis quantile…

Methodology · Statistics 2023-04-17 Andrey Akinshin

The classical concept of inequality curves and measures is extended to conditional inequality curves and measures and a curve of conditional inequality measures is introduced. This extension provides a more nuanced analysis of inequality in…

Statistics Theory · Mathematics 2025-04-23 Alicja Jokiel-Rokita , Sylwester Piątek , Rafał Topolnicki

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…

Methodology · Statistics 2021-11-08 Yingying Zhang , Yuefeng Si , Guodong Li , Chil-Ling Tsai

Quantum Computing offers a new paradigm for efficient computing and many AI applications could benefit from its potential boost in performance. However, the main limitation is the constraint to linear operations that hampers the…

Quantum Physics · Physics 2023-03-10 Antonio Macaluso , Luca Clissa , Stefano Lodi , Claudio Sartori

Quantile regression is a powerful tool for robust and heterogeneous learning that has seen applications in a diverse range of applied areas. However, its broader application is often hindered by the substantial computational demands arising…

Machine Learning · Statistics 2025-08-13 Qian Tang , Yuwen Gu , Boxiang Wang
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