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| Preface | |
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| Introduction | |
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| Means and Ends | |
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| The First Regression: A Historical Prelude | |
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| Quantiles, Ranks, and Optimization | |
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| Preview of Quantile Regression | |
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| Three Examples | |
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| Salaries versus Experience | |
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| Student Course Evaluations and Class Size | |
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| Infant Birth Weight | |
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| Conclusion | |
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| Fundamentals of Quantile Regression | |
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| Quantile Treatment Effects | |
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| How Does Quantile Regression Work? | |
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| Regression Quantiles Interpolate p Observations | |
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| The Subgradient Condition | |
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| Equivariance | |
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| Censoring | |
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| Robustness | |
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| The Influence Function | |
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| The Breakdown Point | |
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| Interpreting Quantile Regression Models | |
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| Some Examples | |
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| Caution: Quantile Crossing | |
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| A Random Coefficient Interpretation | |
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| Inequality Measures and Their Decomposition | |
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| Expectiles and Other Variations | |
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| Interpreting Misspecified Quantile Regressions | |
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| Problems | |
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| Inference for Quantile Regression | |
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| The Finite-Sample Distribution of Regression Quantiles | |
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| A Heuristic Introduction to Quantile Regression Asymptotics | |
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| Confidence Intervals for the Sample Quantiles | |
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| Quantile Regression Asymptotics with IID Errors | |
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| Quantile Regression Asymptotics in Non-IID Settings | |
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| Wald Tests | |
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| Two-Sample Tests of Location Shift | |
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| General Linear Hypotheses | |
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| Estimation of Asymptotic Covariance Matrices | |
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| Scalar Sparsity Estimation | |
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| Covariance Matrix Estimation in Non-IID Settings | |
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| Rank-Based Inference | |
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| Rank Tests for Two-Sample Location Shift | |
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| Linear Rank Statistics | |
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| Asymptotics of Linear Rank Statistics | |
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| Rank Tests Based on Regression Rankscores | |
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| Confidence Intervals Based on Regression Rankscores | |
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| Quantile Likelihood Ratio Tests | |
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| Inference on the Quantile Regression Process | |
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| Wald Processes | |
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| Quantile Likelihood Ratio Processes | |
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| The Regression Rankscore Process Revisited | |
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| Tests of the Location-Scale Hypothesis | |
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| Resampling Methods and the Bootstrap | |
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| Bootstrap Refinements, Smoothing, and Subsampling | |
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| Resampling on the Subgradient Condition | |
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| Monte Carlo Comparison of Methods | |
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| Model 1: A Location-Shift Model | |
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| Model 2: A Location-Scale-Shift Model | |
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| Problems | |
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| Asymptotic Theory of Quantile Regression | |
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| Consistency | |
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| Univariate Sample Quantiles | |
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| Linear Quantile Regression | |
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| Rates of Convergence | |
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| Bahadur Representation | |
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| Nonlinear Quantile Regression | |
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| The Quantile Regression Rankscore Process | |
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| Quantile Regression Asymptotics under Dependent Conditions | |
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| Autoregression | |
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| ARMA Models | |
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| ARCH-like Models | |
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| Extremal Quantile Regression | |
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| The Method of Quantiles | |
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| Model Selection, Penalties, and Large-p Asymptotics | |
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| Model Selection | |
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| Penalty Methods | |
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| Asymptotics for Inference | |
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| Scalar Sparsity Estimation | |
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| Covariance Matrix Estimation | |
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| Resampling Schemes and the Bootstrap | |
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| Asymptotics for the Quantile Regression Process | |
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| The Durbin Problem | |
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| Khmaladization of the Parametric Empirical Process | |
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| The Parametric Quantile Process | |
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| The Parametric Quantile Regression Process | |
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| Problems | |
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| L-Statistics and Weighted Quantile Regression | |
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| L-Statistics for the Linear Model | |
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| Optimal L-Estimators of Location and Scale | |
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| L-Estimation for the Linear Model | |
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| Kernel Smoothing for Quantile Regression | |
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| Kernel Smoothing of the [rho subscript tau]-Function | |
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| Weighted Quantile Regression | |
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| Weighted Linear Quantile Regression | |
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| Estimating Weights | |
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| Quantile Regression for Location-Scale Models | |
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| Weighted Sums of [rho subscript tau]-Functions | |
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| Problems | |
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| Computational Aspects of Quantile Regression | |
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| Introduction to Linear Programming | |
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| Vertices | |
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| Directions of Descent | |
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| Conditions for Optimality | |
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| Complementary Slackness | |
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| Duality | |
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| Simplex Methods for Quantile Regression | |
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| Parametric Programming for Quantile Regression | |
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| Parametric Programming for Regression Rank Tests | |
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| Interior Point Methods for Canonical LPs | |
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| Newton to the Max: An Elementary Example | |
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| Interior Point Methods for Quantile Regression | |
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| Interior vs. Exterior: A Computational Comparison | |
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| Computational Complexity | |
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| Preprocessing for Quantile Regression | |
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| "Selecting" Univariate Quantiles | |
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| Implementation | |
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| Confidence Bands | |
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| Choosing m | |
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| Nonlinear Quantile Regression | |
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| Inequality Constraints | |
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| Weighted Sums of [rho subscript tau]-Functions | |
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| Sparsity | |
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| Conclusion | |
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| Problems | |
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| Nonparametric Quantile Regression | |
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| Locally Polynomial Quantile Regression | |
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| Average Derivative Estimation | |
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| Additive Models | |
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| Penalty Methods for Univariate Smoothing | |
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| Univariate Roughness Penalties | |
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| Total Variation Roughness Penalties | |
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| Penalty Methods for Bivariate Smoothing | |
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| Bivariate Total Variation Roughness Penalties | |
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| Total Variation Penalties for Triograms | |
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| Penalized Triogram Estimation as a Linear Program | |
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| On Triangulation | |
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| On Sparsity | |
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| Automatic [lambda] Selection | |
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| Boundary and Qualitative Constraints | |
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| A Model of Chicago Land Values | |
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| Taut Strings and Edge Detection | |
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| Additive Models and the Role of Sparsity | |
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| Twilight Zone of Quantile Regression | |
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| Quantile Regression for Survival Data | |
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| Quantile Functions or Hazard Functions? | |
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| Censoring | |
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| Discrete Response Models | |
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| Binary Response | |
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| Count Data | |
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| Quantile Autoregression | |
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| Quantile Autoregression and Comonotonicity | |
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| Copula Functions and Nonlinear Quantile Regression | |
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| Copula Functions | |
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| High-Breakdown Alternatives to Quantile Regression | |
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| Multivariate Quantiles | |
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| The Oja Median and Its Extensions | |
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| Half-Space Depth and Directional Quantile Regression | |
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| Penalty Methods for Longitudinal Data | |
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| Classical Random Effects as Penalized Least Squares | |
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| Quantile Regression with Penalized Fixed Effects | |
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| Causal Effects and Structural Models | |
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| Structural Equation Models | |
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| Chesher's Causal Chain Model | |
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| Interpretation of Structural Quantile Effects | |
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| Estimation and Inference | |
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| Choquet Utility, Risk, and Pessimistic Portfolios | |
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| Choquet Expected Utility | |
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| Choquet Risk Assessment | |
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| Pessimistic Portfolios | |
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| Conclusion | |
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| Quantile Regression in R: A Vignette | |
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| Introduction | |
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| What Is a Vignette? | |
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| Getting Started | |
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| Object Orientation | |
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| Formal Inference | |
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| More on Testing | |
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| Inference on the Quantile Regression Process | |
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| Nonlinear Quantile Regression | |
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| Nonparametric Quantile Regression | |
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| Conclusion | |
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| Asymptotic Critical Values | |
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| References | |
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| Name Index | |
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| Subject Index | |