Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. Roger Koenker has devoted more than 25 years of research to the topic. The methods in his analysis are illustrated with a variety of applications from economics, biology, ecology and finance and will target audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above. Author resource page: http://www.econ.uiuc.edu/~roger/research/rq/rq.html
Roger Koenker is the winner of the 2010 Emanuel and Carol Parzen Prize for Statistical Innovation, awarded by the the Department of Statistics at Texas A&M University.
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CHAPTER 1 Introduction
CHAPTER 2 Fundamentals of Quantile Regression
CHAPTER 3 Inference for Quantile Regression
CHAPTER 4 Asymptotic Theory of Quantile Regression
CHAPTER 5 LStatistics and Weighted Quantile Regression
CHAPTER 6 Computational Aspects of Quantile Regression
CHAPTER 7 Nonparametric Quantile Regression
CHAPTER 8 Twilight Zone of Quantile Regression
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algorithm approach asymptotic bandwidth behavior bivariate bootstrap Brownian bridge censoring coefﬁcients compute conditional distribution conditional quantile functions conﬁdence intervals consider constraint set convex covariance matrix covariates deﬁne deﬁnite denotes difﬁcult distribution function dual econometrics efﬁcient empirical distribution function equivariance example ﬁgure ﬁnd ﬁrst ﬁt ﬁtted ﬁtting ﬁxed formulation function F Gaussian hypothesis iid error illustrate inﬂuence interior point interior point methods Koenker L-estimators least-squares estimator linear model linear programming location shift location-scale M-estimators matrix median regression methods minimizing monotone nonlinear nonparametric objective function observations optimal order statistics parameters penalty piecewise linear plot Portnoy primal quadratic quantile regression estimator quantile regression model quantile regression problem quantile regression process quantile treatment effect random variable rankscore regression quantile residuals response result sample quantiles satisﬁes signiﬁcant simple slope smoothing solution solving sparsity speciﬁed sufﬁciently tail test statistic Theorem theory two-sample univariate vector vertex weight zero