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
"Given the substantial impact that Quantile Regression (QR) has had in the statistical literature in general (and particularly in econometrics), a handbook that acknowledges this impact and explores its breadth is especially welcome. This volume provides an excellent coverage of the developments in, and applications of, QR over the past 40 years. A brief historical "memoir" by Bassett and Koenker is followed by 21 chapters contributed by a broad cross-section of scholars, all of whom are experts in QR. These chapters amply illustrate the versatility of QR, and the wide range of variations on its central theme that can be developed to give us a powerful suite of inferential methods…This Handbook is a wonderful resource for graduate students and researchers alike. As has been noted already, the various contributions provide an excellent coverage of the use of QR in the context of a variety of statistical models and types of data. In addition, the book provides illustrations of the application of QR in finance, ecology and environmental sciences, and in genetic and genomic studies. The editors and contributors are to be congratulated on assembling this valuable handbook, which will serve to update and significantly extend our understanding of the richness of QR methods."
—David E. Giles in Statistical Papers, September 2018
"Quantile regression was introduced in 1757 but not perfected until Koenker and Bassett made it a modern tool for robust analyses in linear models in 1978. This book is testimony to its continuing vitality and growing relevance in the big data era."
—Stephen M. Stigler, Ernest DeWitt Burton Distinguished Service Professor of Statistics, University of Chicago
"Since its invention by Koenker and Bassett, quantile regression has moved from intriguing statistical curiosity to a central empirical tool in the applied econometrician's toolkit. This volume offers a valuable, accessible, and timely summary of the many major methodological developments that have expanded and enriched our understanding of quantile regression and its many applications. Many of the volume's contributors have been active in promoting the "quantile revolution." Practitioners and methodologists alike should find the essays in this Handbook useful and interesting."
—Josh Angrist, MIT Department of Economics
"Quantile regression is a generalization of median regression. It is not the usual sum of squares of residuals that is minimized, but the sum of their absolute values. Median regression is known for its robustness. In 1978 Koenker and Basset published a paper in Econometrica in which they introduced regression quantiles. …I have access to eight other handbooks in the CRC series, and this one is by far the most theoretical, with a very high formula density. In places it looks like a handbook of the theory of quantile regression. Under such an umbrella, there is a lot of value to be found (see the table of contents on the publisher’s website). …There are many references at the end of the various chapters, which indicates the popularity of quantile regression. They are a good source for further study."
-Paul Eilers, ISCB June 2018