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Quantile regression. (English) Zbl 1111.62037
Econometric Society Monographs 38. Cambridge: Cambridge University Press (ISBN 0-521-60827-9/pbk; 0-521-84573-4/hbk; 0-511-12816-9/ebook). xv, 349 p. (2005).
Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least-squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale, and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods are illustrated with a variety of applications from economics, biology, ecology, and finance. The treatment will find its core audiences in econometrics, statistics, and biostatistics. The book offers the opportunity for a more complete view of the statistical landscape and the relationships among stochastic variables. Just as minimizing sums of squares permits us to estimate a wide variety of models for conditional mean functions, minimizing a simple asymmetric version of absolute errors yields estimates for conditional quantile functions.
The Contents of the book are as follows: 1. Introduction; 2. Fundamentals of Quantile Regression; 3. Inference for Quantile Regression; 4. Asymptotic Theory of Quantile Regression; 5. L-Statistics and Weighted Quantile Regression; 6. Computational Aspects of Quantile Regression; 7. Nonparametric Quantile Regression; 8. Twilight Zone of Quantile Regression; 9. Conclusions. At the end, before the References, Name Index and Subject Index, there are also two Appendices: A. Quantile Regression in R: A Vignette; B. Asymptotic Critical Values.
This book can provide a comprehensive introduction to quantile regression methods and it will serve to stimulate others to explore and further develop these ideas in their own research. Statistical software for quantile regression is now widely available in many well-known statistical packages.

MSC:
62G08 Nonparametric regression and quantile regression
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62F99 Parametric inference
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62P20 Applications of statistics to economics
62P10 Applications of statistics to biology and medical sciences; meta analysis
Software:
quantreg; R
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