Quantile regression:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Edition: | 1. publ., transferred to digital print. |
| Series: | Econometric Society monographs
38 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [319] - 335 |
| Physical Description: | XV, 349 S. graph. Darst. |
| ISBN: | 0521845734 0521608279 9780521845731 9780521608275 |
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Record in the Search Index
| _version_ | 1804138556073967616 |
|---|---|
| adam_text | Contents
Preface
page
xiii
1
Introduction
1
1.1
Means and Ends
1
1.2
The First Regression: A Historical Prelude
2
1.3
Quantiles, Ranks, and Optimization
5
1.4
Preview of Quantile Regression
9
1.5
Three Examples
13
1.5.1
Salaries versus Experience
13
1.5.2
Student Course Evaluations and Class Size
17
1.5.3
Infant Birth Weight
20
1.6
Conclusion
25
2
Fundamentals of Quantile Regression
26
2.1
Quantile Treatment Effects
26
2.2
How Does Quantile Regression Work?
32
2.2.1
Regression Quantiles Interpolate
ρ
Observations
33
2.2.2
The
Subgradient
Condition
34
2.2.3
Equivariance
38
2.2.4
Censoring
40
2.3
Robustness 42
2.3.1
The Influence Function
42
2.3.2
The Breakdown Point 45
2.4
Interpreting Quantile Regression Models
47
2.4.1
Some Examples 48
2.5
Caution: Quantile Crossing
55
2.6
A Random Coefficient Interpretation
59
2.7
Inequality Measures and Their Decomposition
62
2.8
Expectiles and Other Variations 63
2.9
Interpreting Misspecified Quantile Regressions
65
2.10
Problems
66
viii Contents
3
Inference for Quantile Regression
68
3.1
The Finite-Sample Distribution of Regression Quantiles
68
3.2
A Heuristic Introduction to Quantile Regression
Asymptotics
71
3.2.1
Confidence Intervals for the Sample Quantiles
72
3.2.2
Quantile Regression Asymptotics with IID Errors
73
3.2.3
Quantile Regression Asymptotics in Non-IID
Settings
74
3.3 Wald
Tests
75
3.3.1
Two-Sample Tests of Location Shift
75
3.3.2
General Linear Hypotheses
76
3.4
Estimation of Asymptotic Covariance Matrices
77
3.4.1
Scalar Sparsity Estimation
77
3.4.2
Covariance Matrix Estimation in Non-IID Settings
79
3.5
Rank-Based Inference
81
3.5.1
Rank Tests for Two-Sample Location Shift
81
3.5.2
Linear Rank Statistics
84
3.5.3
Asymptotics of Linear Rank Statistics
85
3.5.4
Rank Tests Based on Regression Rankscores
87
3.5.5
Confidence Intervals Based on Regression
Rankscores
91
3.6
Quantile Likelihood Ratio Tests
92
3.7
Inference on the Quantile Regression Process
95
3.7.1 Wald
Processes
97
3.7.2
Quantile Likelihood Ratio Processes
98
3.7.3
The Regression Rankscore Process Revisited
98
3.8
Tests of the Location-Scale Hypothesis
98
3.9
Resampling Methods and the Bootstrap
105
3.9.1
Bootstrap Refinements, Smoothing, and
Subsampling
107
3.9.2
Resampling on the
Subgradient
Condition
108
3.10
Monte Carlo Comparison of Methods
110
3.10.1 Modell:
A Location-Shift Model 111
3.10.2
Model
2:
A Location-Scale-Shift Model
112
3.11
Problems
113
4
Asymptotic Theory of Quantile Regression
116
4.1
Consistency
117
4.1.1
Univariate Sample Quantiles
117
4.1.2
Linear Quantile Regression
118
4.2
Rates of Convergence
120
4.3
Bahadur Representation
122
4.4
Nonlinear Quantile Regression
123
4.5
The Quantile Regression Rankscore Process
124
4.6
Quantile Regression Asymptotics under Dependent
Conditions
126
Contents ix
4.6.1 Autoregression 126
4.6.2
ARMA
Models 128
4.6.3 ARCH-like Models 129
4.7
Extremal
Quantile Regression 130
4.8
The Method of Quantiles
131
4.9 Model
Selection, Penalties,
and Large-p Asymptotics 133
4.9.1 Model
Selection
134
4.9.2 Penalty
Methods
135
4.10 Asymptotics
for Inference 1
38
4.10.1
Scalar Sparsity Estimation
139
4.10.2 Covariance Matrix
Estimation
141
4.11
Resampling Schemes and the Bootstrap
141
4.12
Asymptotics for the Quantile Regression Process
142
4.12.1
The
Durbin
Problem
142
4.12.2
Khmaladization of the Parametric Empirical
Process
144
4.12.3
The Parametric Quantile Process
145
4.12.4
The Parametric Quantile Regression Process
146
4.13
Problems
149
5
L-Statistics and Weighted Quantile Regression
151
5.1
L-Statistics for the Linear Model
151
5.1.1
Optimal L-Estimators of Location and Scale
153
5.1.2
L-Estimation for the Linear Model
155
5.2
Kernel Smoothing for Quantile Regression
158
5.2.1
Kernel Smoothing of the pT-Function
160
5.3
Weighted Quantile Regression
160
5.3.1
Weighted Linear Quantile Regression
160
5.3.2
Estimating Weights
161
5.4
Quantile Regression for Location-Scale Models
164
5.5
Weighted Sums of pr-Functions
168
5.6
Problems
170
6
Computational Aspects of Quantile Regression
173
6.1
Introduction to Linear Programming
173
6.1.1
Vertices
174
6.1.2
Directions of Descent
176
6.1.3
Conditions for Optimality
177
6.1.4
Complementary Slackness
178
6.1.5
Duality 18°
6.2
Simplex Methods for Quantile Regression
181
6.3
Parametric Programming for Quantile Regression
185
6.3.1
Parametric Programming for Regression
Rank Tests 188
6.4
Interior Point Methods for Canonical LPs
190
6.4.1
Newton to the Max: An Elementary Example
193
6.4.2
Interior Point Methods for Quantile Regression
199
ic
Contents
6.4.3
Interior
vs. Exterior: A Computational
Comparison
202
6.4.4
Computational Complexity
204
6.5
Preprocessing for Quantile Regression
206
6.5.1
Selecting Univariate Quantiles
207
6.5.2
Implementation
207
6.5.3
Confidence Bands
208
6.5.4
Choosing
m
209
6.6
Nonlinear Quantile Regression
211
6.7
Inequality Constraints
213
6.8
Weighted Sums of
ρτ
-Functions
214
6.9
Sparsity
216
6.10
Conclusion
220
6.11
Problems
220
7
Nonparametric Quantile Regression
222
7.1
Locally Polynomial Quantile Regression
222
7.1.1
Average Derivative Estimation
226
7.1.2
Additive Models
228
7.2
Penalty Methods for Univariate Smoothing
229
7.2.1
Univariate Roughness Penalties
229
7.2.2
Total Variation Roughness Penalties
230
7.3
Penalty Methods for Bivariate Smoothing
235
7.3.1
Bivariate Total Variation Roughness Penalties
235
7.3.2
Total Variation Penalties for Triograms
236
7.3.3
Penalized
Triogram
Estimation as a Linear
Program
240
7.3.4
On
Triangulation
241
7.3.5
On Sparsity
242
7.3.6
Automatic
λ
Selection
242
7.3.7
Boundary and Qualitative Constraints
243
7.3.8
A Model of Chicago Land Values
243
7.3.9
Taut Strings and Edge Detection
246
7.4
Additive Models and the Role of Sparsity
248
8
Twilight Zone of Quantile Regression
250
8.1
Quantile Regression for Survival Data
250
8.1.1
Quantile Functions or Hazard Functions?
252
8.1.2
Censoring
253
8.2
Discrete Response Models
255
8.2.1
Binary Response
255
8.2.2
Count Data
259
8.3
Quantile
Autoregression 260
8.3.1
Quantile
Autoregression
and Comonotonicity
261
8.4
Copula Functions and Nonlinear Quantile Regression
265
8.4.1
Copula Functions
265
Contents xi
8.5
High-Breakdown
Alternatives
to Quantile
Regression 268
8.6 Multivariate Quantiles 272
8.6.1 The Oja
Median and Its Extensions
273
8.6.2
Half-Space Depth and Directional Quantile
Regression
275
8.7
Penalty Methods for Longitudinal Data
276
8.7.1
Classical Random Effects as Penalized
Least Squares
276
8.7.2
Quantile Regression with Penalized Fixed Effects
278
8.8
Causal Effects and Structural Models
281
8.8.1
Structural Equation Models
281
8.8.2
Chesher s Causal Chain Model
283
8.8.3
Interpretation of Structural Quantile Effects
284
8.8.4
Estimation and Inference
285
8.9
Choquet Utility, Risk, and Pessimistic Portfolios
287
8.9.1
Choquet Expected Utility
287
8.9.2
Choquet Risk Assessment
289
8.9.3
Pessimistic Portfolios
291
9
Conclusion
293
A Quantile Regression in R: A Vignette
295
A.
1
Introduction
295
A.2 What Is a Vignette?
296
A.3 Getting Started
296
A.4 Object Orientation
298
A.5 Formal Inference
299
A.6 More on Testing
305
A.7 Inference on the Quantile Regression Process
307
A.8 Nonlinear Quantile Regression
308
A.9 Nonparametric Quantile Regression
310
A.
10
Conclusion
316
В
Asymptotic Critical Values
317
References
319
Name Index
337
Subject Index
342
|
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| id | DE-604.BV035269120 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:04Z |
| institution | BVB |
| isbn | 0521845734 0521608279 9780521845731 9780521608275 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017074521 |
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| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-739 |
| owner_facet | DE-355 DE-BY-UBR DE-739 |
| physical | XV, 349 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Econometric Society monographs |
| series2 | Econometric Society monographs |
| spelling | Koenker, Roger 1947- Verfasser (DE-588)131874632 aut Quantile regression Roger Koenker 1. publ., transferred to digital print. Cambridge [u.a.] Cambridge Univ. Press 2008 XV, 349 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Econometric Society monographs 38 Literaturverz. S. [319] - 335 Regression analysis Mathematical statistics Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Quantil (DE-588)4224812-7 gnd rswk-swf Regressionsanalyse (DE-588)4129903-6 s Quantil (DE-588)4224812-7 s DE-604 Econometric Society monographs 38 (DE-604)BV000018129 38 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017074521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Koenker, Roger 1947- Quantile regression Econometric Society monographs Regression analysis Mathematical statistics Regressionsanalyse (DE-588)4129903-6 gnd Quantil (DE-588)4224812-7 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4224812-7 |
| title | Quantile regression |
| title_auth | Quantile regression |
| title_exact_search | Quantile regression |
| title_full | Quantile regression Roger Koenker |
| title_fullStr | Quantile regression Roger Koenker |
| title_full_unstemmed | Quantile regression Roger Koenker |
| title_short | Quantile regression |
| title_sort | quantile regression |
| topic | Regression analysis Mathematical statistics Regressionsanalyse (DE-588)4129903-6 gnd Quantil (DE-588)4224812-7 gnd |
| topic_facet | Regression analysis Mathematical statistics Regressionsanalyse Quantil |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017074521&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018129 |
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