Quantile Regression
By: Roger Koenker, Andrew Chesher (Editor), Matthew Jackson (Editor)
Paperback | 21 July 2005
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366 Pages
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orThe methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.
About the Author
Roger Koenker is McKinley Professor of Economics and Professor of Statistics at the University of Illinois at Urbana-Champaign. From 1976 to 1983 he was a member of the technical staff at Bell Laboratories. He has held visiting positions at The University of Pennsylvania, Charles University, Prague, Nuffield College, Oxford, University College London and Australian National University. He is a Fellow of the Econometric Society.
Industry Reviews
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 |
Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780521608275
ISBN-10: 0521608279
Series: Econometric Society Monographs
Published: 21st July 2005
Format: Paperback
Language: English
Number of Pages: 366
Audience: Professional and Scholarly
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 14.99 x 2.54
Weight (kg): 0.54
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