Handbook of Quantile Regression

Roger Koenker, University of IllinoisVictor Chernozhukov, MITXuming 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

• A Quantile Regression Memoir - Gilbert W. Bassett Jr. and Roger KoenkerResampling Methods - Xuming HeQuantile Regression: Penalized - Ivan MizeraBayesian Quantile Regression - Huixia Judy Wang and Yunwen YangComputational Methods for Quantile Regression - Roger KoenkerSurvival Analysis: A Quantile Perspective - Zhiliang Ying and Tony SitQuantile Regression for Survival Analysis - Limin PengSurvival Analysis with Competing Risks and Semi-competing Risks Data - Ruosha Li and Limin PengInstrumental Variable Quantile Regression - Victor Chernozhukov, Christian Hansen, and Kaspar WuethrichLocal Quantile Treatment Effects - Blaise Melly and Kaspar WuethrichQuantile Regression with Measurement Errors and Missing Data - Ying WeiMultiple-Output Quantile Regression - Marc Hallin and Miroslav SimanSample Selection in Quantile Regression: A Survey - Manuel Arellano and Stephane BonhommeNonparametric Quantile Regression for Banach-valued Response - Joydeep Chowdhury and Probal ChaudhuriHigh-Dimensional Quantile Regression - Alexandre Belloni, Victor Chernozhukov, and Kengo KatoNonconvex Penalized Quantile Regression: A Review of Methods, Theory and Algorithms - Lan WangQAR and Quantile Time Series Analysis - Zhijie XiaoExtremal Quantile Regression -Victor Chernozhukov, Ivan Fernandez-Val, and Tetsuya KajiQuantile regression methods for longitudinal data - Antonio F. Galvao and Kengo KatoQuantile Regression Applications in Finance - Oliver Linton and Zhijie XiaoQuantile regression for Genetic and Genomic Applications - Laurent Briollais and Gilles DurrieuQuantile regression applications in ecology and the environmental sciences - Brian S. Cade