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.
Table of Contents
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
Roger Koenker, University of Illinois
Victor Chernozhukov, MIT
Xuming He, University of Michigan
Limin Peng, Emory University