Part I. Introduction: 1. Means and ends; 2. The first regression: an historical prelude; 3. Quantiles, ranks, and optimization; 4. Preview of quantile regression; 5. Three examples; 6. Conclusion; Part II.
Fundamentals of Quantile Regression: 7. Quantile treatment effects; 8. How does quantile regression work?; 9. Robustness; 10. Interpreting quantile regression models; 11. Caution: quantile crossing; 12. A random coefficient interpretation; 13. Inequality measures and their decomposition; 14.
Expectiles and other variations; 15. Interpreting misspecified quantile regressions; 16. Problems; Part III. Inference for Quantile Regression: 17. The finite sample distribution of regression quantiles; 18. A heuristic introduction to quantile regression asymptotics; 19. Wald tests; 20. Estimation of asymptotic covariance matrices; 21.
Rank based Inference for quantile regression; 22. Quantile likelihood ratio tests; 23. Inference on the quantile regression process; 24. Tests of the location/acale hypothesis; 25. Resampling methods and the bootstrap; 26. Monte-Carlo comparison of methods; 27. Problems; Part IV. Asymptotic Theory of Quantile Regression: 28.
Consistency; 29. Rates of convergence; 30. Bahadur representation; 31. Nonlinear quantile regression; 32. The quantile regression rankscore process; 33. Quantile regression asymptotics under dependent conditions; 34. Extremal quantile regression; 35. The method of quantiles; 36.
Model selection, penalties, and large-p asymptotics; 37. Asymptotics for inference; 38. Resampling schemes and the bootstrap; 39. Asymptotics for the quantile regression process; 40. Problems; Part V. L-Statistics and Weighted Quantile Regression: 41. L-Statistics for the linear model; 42. Kernel smoothing for quantile regression; 43.
Weighted quantile regression; 44 Quantile regression for location-scale models; 45. Weighted sums of p-functions; 46. Problems; Part VI. Computational Aspects of Quantile Regression: 47. Introduction to linear programming; 48. Simplex methods for quantile regression; 49. Parametric programming for quantile regression; 50 Interior point methods for canonical LPs; 51. Preprocessing for quantile regression; 52.
Nonlinear quantile regression; 53. Inequality constraints; 54. Weighted sums of p-functions; 55. Sparsity; 56. Conclusion; 57. Problems; Part VII. Nonparametric Quantile Regression: 58. Locally polynomial quantile regression; 59.
Penalty methods for univariate smoothing; 60. Penalty methods for bivariate Smoothing; 61. Additive models and the Role of sparsity; Part VIII. Twilight Zone of Quantile Regression: 62. Quantile regression for survival data; 63. Discrete Response models; 64. Quantile autoregression; 65. Copula functions and nonlinear quantile regression; 66.
High breakdown alternatives to quantile regression; 67. Multivariate quantiles; 68. Penalty methods for longitudinal data; 69. Causal effects and structural models; 70. Choquet utility, risk and pessimistic portfolios; Part IX. Conclusion: A. Quantile regression in R: a vignette; A.1.
Introduction; A.2. What is a vignette?; A.3. Getting started; A.4. Object orientation; A.5.
Formal Inference; A.6. More on testing; A.7. Inference on the quantile regression process; A.8. Nonlinear quantile regression; A.9.
Nonparametric quantile regression; A.10. Conclusion; B. Asymptotic critical values.