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Quantile Regression

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Part of Econometric Society Monographs

  • Date Published: October 2005
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511128165

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About the Authors
  • 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: 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.

    • First comprehensive study of quantile regression methods
    • Tutorial on associated statistical software in R
    • Illustrative applications from a broad variety of disciplines
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    Reviews & endorsements

    "Roger Koenker has a profound knowledge of econometrics, linear and non-linear programming, statistics and computational statistics, and a strong intuition, combined with a sense for practical problems. As a result, this excellent book combines all of these above aspects and covers a broad spectrum, from practical applications to the weak convergence of probability measures through examples on maximum daily temperatures to Choquet capacities...this book should definitely be on every statistician's and econometrician's shelf."
    Jana Jureckova, Journal of the American Statistical Association

    "The author is one [of] the "fathers" of quantile regression. He has substantially contributed to the theoretical as well as the applied development of the field. The book is well written... It provides useful information for statisticians and econometricians, and it can certainly serve as a reference book."
    M. Huskova, Mathematical Reviews

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    Product details

    • Date Published: October 2005
    • format: Adobe eBook Reader
    • isbn: 9780511128165
    • contains: 63 b/w illus. 13 tables 20 exercises
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    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.

  • Author

    Roger Koenker, University of Illinois, Urbana-Champaign
    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.

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