| Preface | p. xiii |
| Introduction | p. 1 |
| Means and Ends | p. 1 |
| The First Regression: A Historical Prelude | p. 2 |
| Quantiles, Ranks, and Optimization | p. 5 |
| Preview of Quantile Regression | p. 9 |
| Three Examples | p. 13 |
| Salaries versus Experience | p. 13 |
| Student Course Evaluations and Class Size | p. 17 |
| Infant Birth Weight | p. 20 |
| Conclusion | p. 25 |
| Fundamentals of Quantile Regression | p. 26 |
| Quantile Treatment Effects | p. 26 |
| How Does Quantile Regression Work? | p. 32 |
| Regression Quantiles Interpolate p Observations | p. 33 |
| The Subgradient Condition | p. 34 |
| Equivariance | p. 38 |
| Censoring | p. 40 |
| Robustness | p. 42 |
| The Influence Function | p. 42 |
| The Breakdown Point | p. 45 |
| Interpreting Quantile Regression Models | p. 47 |
| Some Examples | p. 48 |
| Caution: Quantile Crossing | p. 55 |
| A Random Coefficient Interpretation | p. 59 |
| Inequality Measures and Their Decomposition | p. 62 |
| Expectiles and Other Variations | p. 63 |
| Interpreting Misspecified Quantile Regressions | p. 65 |
| Problems | p. 66 |
| Inference for Quantile Regression | p. 68 |
| The Finite-Sample Distribution of Regression Quantiles | p. 68 |
| A Heuristic Introduction to Quantile Regression Asymptotics | p. 71 |
| Confidence Intervals for the Sample Quantiles | p. 72 |
| Quantile Regression Asymptotics with IID Errors | p. 73 |
| Quantile Regression Asymptotics in Non-IID Settings | p. 74 |
| Wald Tests | p. 75 |
| Two-Sample Tests of Location Shift | p. 75 |
| General Linear Hypotheses | p. 76 |
| Estimation of Asymptotic Covariance Matrices | p. 77 |
| Scalar Sparsity Estimation | p. 77 |
| Covariance Matrix Estimation in Non-IID Settings | p. 79 |
| Rank-Based Inference | p. 81 |
| Rank Tests for Two-Sample Location Shift | p. 81 |
| Linear Rank Statistics | p. 84 |
| Asymptotics of Linear Rank Statistics | p. 85 |
| Rank Tests Based on Regression Rankscores | p. 87 |
| Confidence Intervals Based on Regression Rankscores | p. 91 |
| Quantile Likelihood Ratio Tests | p. 92 |
| Inference on the Quantile Regression Process | p. 95 |
| Wald Processes | p. 97 |
| Quantile Likelihood Ratio Processes | p. 98 |
| The Regression Rankscore Process Revisited | p. 98 |
| Tests of the Location-Scale Hypothesis | p. 98 |
| Resampling Methods and the Bootstrap | p. 105 |
| Bootstrap Refinements, Smoothing, and Subsampling | p. 107 |
| Resampling on the Subgradient Condition | p. 108 |
| Monte Carlo Comparison of Methods | p. 110 |
| Model 1: A Location-Shift Model | p. 111 |
| Model 2: A Location-Scale-Shift Model | p. 112 |
| Problems | p. 113 |
| Asymptotic Theory of Quantile Regression | p. 116 |
| Consistency | p. 117 |
| Univariate Sample Quantiles | p. 117 |
| Linear Quantile Regression | p. 118 |
| Rates of Convergence | p. 120 |
| Bahadur Representation | p. 122 |
| Nonlinear Quantile Regression | p. 123 |
| The Quantile Regression Rankscore Process | p. 124 |
| Quantile Regression Asymptotics under Dependent Conditions | p. 126 |
| Autoregression | p. 126 |
| ARMA Models | p. 128 |
| ARCH-like Models | p. 129 |
| Extremal Quantile Regression | p. 130 |
| The Method of Quantiles | p. 131 |
| Model Selection, Penalties, and Large-p Asymptotics | p. 133 |
| Model Selection | p. 134 |
| Penalty Methods | p. 135 |
| Asymptotics for Inference | p. 138 |
| Scalar Sparsity Estimation | p. 139 |
| Covariance Matrix Estimation | p. 141 |
| Resampling Schemes and the Bootstrap | p. 141 |
| Asymptotics for the Quantile Regression Process | p. 142 |
| The Durbin Problem | p. 142 |
| Khmaladization of the Parametric Empirical Process | p. 144 |
| The Parametric Quantile Process | p. 145 |
| The Parametric Quantile Regression Process | p. 146 |
| Problems | p. 149 |
| L-Statistics and Weighted Quantile Regression | p. 151 |
| L-Statistics for the Linear Model | p. 151 |
| Optimal L-Estimators of Location and Scale | p. 153 |
| L-Estimation for the Linear Model | p. 155 |
| Kernel Smoothing for Quantile Regression | p. 158 |
| Kernel Smoothing of the [rho subscript tau]-Function | p. 160 |
| Weighted Quantile Regression | p. 160 |
| Weighted Linear Quantile Regression | p. 160 |
| Estimating Weights | p. 161 |
| Quantile Regression for Location-Scale Models | p. 164 |
| Weighted Sums of [rho subscript tau]-Functions | p. 168 |
| Problems | p. 170 |
| Computational Aspects of Quantile Regression | p. 173 |
| Introduction to Linear Programming | p. 173 |
| Vertices | p. 174 |
| Directions of Descent | p. 176 |
| Conditions for Optimality | p. 177 |
| Complementary Slackness | p. 178 |
| Duality | p. 180 |
| Simplex Methods for Quantile Regression | p. 181 |
| Parametric Programming for Quantile Regression | p. 185 |
| Parametric Programming for Regression Rank Tests | p. 188 |
| Interior Point Methods for Canonical LPs | p. 190 |
| Newton to the Max: An Elementary Example | p. 193 |
| Interior Point Methods for Quantile Regression | p. 199 |
| Interior vs. Exterior: A Computational Comparison | p. 202 |
| Computational Complexity | p. 204 |
| Preprocessing for Quantile Regression | p. 206 |
| "Selecting" Univariate Quantiles | p. 207 |
| Implementation | p. 207 |
| Confidence Bands | p. 208 |
| Choosing m | p. 209 |
| Nonlinear Quantile Regression | p. 211 |
| Inequality Constraints | p. 213 |
| Weighted Sums of [rho subscript tau]-Functions | p. 214 |
| Sparsity | p. 216 |
| Conclusion | p. 220 |
| Problems | p. 220 |
| Nonparametric Quantile Regression | p. 222 |
| Locally Polynomial Quantile Regression | p. 222 |
| Average Derivative Estimation | p. 226 |
| Additive Models | p. 228 |
| Penalty Methods for Univariate Smoothing | p. 229 |
| Univariate Roughness Penalties | p. 229 |
| Total Variation Roughness Penalties | p. 230 |
| Penalty Methods for Bivariate Smoothing | p. 235 |
| Bivariate Total Variation Roughness Penalties | p. 235 |
| Total Variation Penalties for Triograms | p. 236 |
| Penalized Triogram Estimation as a Linear Program | p. 240 |
| On Triangulation | p. 241 |
| On Sparsity | p. 242 |
| Automatic [lambda] Selection | p. 242 |
| Boundary and Qualitative Constraints | p. 243 |
| A Model of Chicago Land Values | p. 243 |
| Taut Strings and Edge Detection | p. 246 |
| Additive Models and the Role of Sparsity | p. 248 |
| Twilight Zone of Quantile Regression | p. 250 |
| Quantile Regression for Survival Data | p. 250 |
| Quantile Functions or Hazard Functions? | p. 252 |
| Censoring | p. 253 |
| Discrete Response Models | p. 255 |
| Binary Response | p. 255 |
| Count Data | p. 259 |
| Quantile Autoregression | p. 260 |
| Quantile Autoregression and Comonotonicity | p. 261 |
| Copula Functions and Nonlinear Quantile Regression | p. 265 |
| Copula Functions | p. 265 |
| High-Breakdown Alternatives to Quantile Regression | p. 268 |
| Multivariate Quantiles | p. 272 |
| The Oja Median and Its Extensions | p. 273 |
| Half-Space Depth and Directional Quantile Regression | p. 275 |
| Penalty Methods for Longitudinal Data | p. 276 |
| Classical Random Effects as Penalized Least Squares | p. 276 |
| Quantile Regression with Penalized Fixed Effects | p. 278 |
| Causal Effects and Structural Models | p. 281 |
| Structural Equation Models | p. 281 |
| Chesher's Causal Chain Model | p. 283 |
| Interpretation of Structural Quantile Effects | p. 284 |
| Estimation and Inference | p. 285 |
| Choquet Utility, Risk, and Pessimistic Portfolios | p. 287 |
| Choquet Expected Utility | p. 287 |
| Choquet Risk Assessment | p. 289 |
| Pessimistic Portfolios | p. 291 |
| Conclusion | p. 293 |
| Quantile Regression in R: A Vignette | p. 295 |
| Introduction | p. 295 |
| What Is a Vignette? | p. 296 |
| Getting Started | p. 296 |
| Object Orientation | p. 298 |
| Formal Inference | p. 299 |
| More on Testing | p. 305 |
| Inference on the Quantile Regression Process | p. 307 |
| Nonlinear Quantile Regression | p. 308 |
| Nonparametric Quantile Regression | p. 310 |
| Conclusion | p. 316 |
| Asymptotic Critical Values | p. 317 |
| References | p. 319 |
| Name Index | p. 337 |
| Subject Index | p. 342 |
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