Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss.

Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments.

The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings.

The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.

The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.

A Quantile Regression Memoir - Gilbert W. Bassett Jr. and Roger Koenker

Resampling Methods - Xuming He

Quantile Regression: Penalized - Ivan Mizera

Bayesian Quantile Regression - Huixia Judy Wang and Yunwen Yang

Computational Methods for Quantile Regression - Roger Koenker

Survival Analysis: A Quantile Perspective - Zhiliang Ying and Tony Sit

Quantile Regression for Survival Analysis - Limin Peng

Survival Analysis with Competing Risks and Semi-competing Risks Data - Ruosha Li and Limin Peng

Instrumental Variable Quantile Regression - Victor Chernozhukov, Christian Hansen, and Kaspar Wuethrich

Local Quantile Treatment Effects - Blaise Melly and Kaspar Wuethrich

Quantile Regression with Measurement Errors and Missing Data - Ying Wei

Multiple-Output Quantile Regression - Marc Hallin and Miroslav Siman

Sample Selection in Quantile Regression: A Survey - Manuel Arellano and Stephane Bonhomme

Nonparametric Quantile Regression for Banach-valued Response - Joydeep Chowdhury and Probal Chaudhuri

High-Dimensional Quantile Regression - Alexandre Belloni, Victor Chernozhukov, and Kengo Kato

Nonconvex Penalized Quantile Regression: A Review of Methods, Theory and Algorithms - Lan Wang

QAR and Quantile Time Series Analysis - Zhijie Xiao

Extremal Quantile Regression -Victor Chernozhukov, Ivan Fernandez-Val, and Tetsuya Kaji

Quantile regression methods for longitudinal data - Antonio F. Galvao and Kengo Kato

Quantile Regression Applications in Finance - Oliver Linton and Zhijie Xiao

Quantile regression for Genetic and Genomic Applications - Laurent Briollais and Gilles Durrieu

Quantile regression applications in ecology and the environmental sciences - Brian S. Cade