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Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to…mehr
Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The 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.
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Autorenporträt
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.
Inhaltsangabe
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.
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.
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.
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.
Rezensionen
'... well written and easy to read, with useful illustrations of important aspects of quantile regression. It is obvious that the author knows the subject inside out, giving an up-to-date, exhaustive account of the subject. ... The book is a valuable contribution to the statistical literature, and a must have for every statistician or econometrician interested in quantile regression methods.' Journal of the Royal Statistical Society
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