Handbook of quantile regression:
Gespeichert in:
| Weitere beteiligte Personen: | , , , |
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| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton
CRC Press
[2018]
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| Schriftenreihe: | Handbooks of modern statistical methods
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| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029909072&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Includes bibliographical references and index |
| Umfang: | xix, 463 Seiten Diagramme |
| ISBN: | 9781498725286 |
Internformat
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| 245 | 1 | 0 | |a Handbook of quantile regression |c edited by Roger Koenker, Victor Chernozhukov, Xuming He, Limin Peng |
| 264 | 1 | |a Boca Raton |b CRC Press |c [2018] | |
| 264 | 4 | |c © 2018 | |
| 300 | |a xix, 463 Seiten |b Diagramme | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Handbooks of modern statistical methods | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Quantile regression | |
| 650 | 4 | |a Regression analysis | |
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| 700 | 1 | |a Chernozhukov, Victor |0 (DE-588)129354759 |4 edt | |
| 700 | 1 | |a He, Xuming |d ca. 20/21. Jahrhundert |0 (DE-588)170895238 |4 edt | |
| 700 | 1 | |a Peng, Limin |0 (DE-588)136267823 |4 edt | |
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Datensatz im Suchindex
| _version_ | 1819278643927449600 |
|---|---|
| adam_text | Contents
Preface xvii
Contributors xix
I Introduction 1
1 A Quantile Regression Memoir 3
Gilbert W. Bassett Jr. and Roger Koenker
1.1 Long ago................................................................. 3
2 Resampling Methods 7
Xuming He
2.1 Introduction ............................................................ 7
2.2 Paired bootstrap......................................................... 8
2.3 Residual-based bootstrap ................................................ 9
2.4 Generalized bootstrap . ................................................ 11
2.5 Estimating function bootstrap ........................................ 11
2.6 Markov chain marginal bootstrap ........................................ 12
2.7 Resampling methods for clustered data ........................... 13
2.8 Resampling methods for censored quantile regression .................... 14
2.9 Bootstrap for post-model selection inference ........................... 15
3 Quantile Regression: Penalized 21
Ivan Mizera
3.1 Penalized: how? ........................................................ 21
3.1.1 A probability path............................................... 21
3.1.2 Regularization of ill-posed problems............................. 22
3.2 Penalized: what?........................................................ 23
3.2.1 The finite differences of Whittaker and others.......... 23
3.2.2 Functions and their derivatives.................................. 24
3.2.3 Quantile regression with smoothing splines....................... 26
3.2.4 Quantile smoothing splines....................................... 28
3.2.5 Total-variation splines.......................................... 29
3.3 Penalized: what else? ................................................ 31
3.3.1 Tuning........................................................... 31
3.3.2 Multiple covariates.............................................. 32
3.3.3 Additive fits, confidence bandaids, and other phantasmagorias ... 34
4 Bayesian Quantile Regression 41
Huixia Judy Wang and Yunwen Yang
4.1 Introduction ........................................................... 41
4.2 Asymmetric Laplace likelihood........................................... 42
4.3 Empirical likelihood.................................................... 45
ix
x Contents
4.4 Nonparametric and semiparametric likelihoods.............................. 47
4.4.1 Mixture-type likelihood............................................. 47
4.4.2 Approximate likelihood via quantile process...................... 49
4.5 Discussion ................................................................ 51
5 Computational Methods for Quantile Regression 55
Roger Koenker
5.1 Introduction ........................................................... 55
5.2 Exterior point methods ................................................ . 57
5.3 Interior point methods ................................................. 58
5.4 Preprocessing .......................................................... 60
5.5 First-order, proximal methods .......................................... 61
5.5.1 Proximal operators and the Moreau envelope....................... 61
5.5.2 Alternating direction method of multipliers......................... 64
5.5.3 Proximal performance................................................ 65
6 Survival Analysis: A Quantile Perspective 69
Zhiliang Ying and Tony Sit
6.1 Introduction ........................................................... 69
6.1.1 Notation......................................................... 70
6.1.2 Censoring........................................................ 71
6.2 Important models ....................................................... 72
6.2.1 Parametric models................................................ 72
6.2.2 Nonparametric estimators......................................... 73
6.2.2.1 Kaplan-Meier estimator.................................. 73
6.2.2.2 Nelson-Aalen estimator.................................. 75
6.2.3 Regression models................................................ 75
6.2.3.1 Cox proportional hazards model.......................... 75
6.2.3.2 Accelerated failure time model.......................... 76
6.2.3.3 Aalen additive hazard model.............................. 78
6.3 Quantile estimation based on censored data.............................. 79
6.3.1 Quantile estimation.............................................. 79
6.3.2 Median and quantile regression...................................... 80
6.3.3 Discussion and miscellanea.......................................... 82
7 Quantile Regression for Survival Analysis 89
Limin Peng
7.1 Introduction .............................................................. 89
7.2 Quantile regression for randomly censored data............................. 90
7.2.1 Random right censoring with C always known ......................... 90
7.2.2 Covariate-independent random right censoring........................ 91
7.2.3 Standard random right censoring..................................... 92
7.2.3.1 Approaches based on the principle of self-consistency ... 92
7.2.3.2 Martingale-based approach.................................. 93
7.2.3.3 Locally weighted method.................................... 94
7.2.4 Variance estimation and other inference............................. 95
7.2.4.1 Variance estimation........................................ 95
7.2.4.2 Second-stage inference..................................... 96
7.2.4.3 Model checking............................................. 96
7.3 Quantile regression in other survival settings ............................ 97
7.3.1 Known random left censoring and/or left truncation.................. 97
Contents xi
7.3.2 Censored data with a survival cure fraction......................... 98
7.4 An illustration of quantile regression for survival analysis ............. 98
8 Survival Analysis with Competing Risks and Semi-competing Risks Data 105
Ruosha Li and Limin Peng
8.1 Competing risks data .................................................... 105
8.1.1 Introduction ...................................................... 105
8.1.2 Cumulative incidence quantile regression........................... 106
8.1.3 Data analysis example.............................................. 108
8.1.4 Marginal quantile regression....................................... 110
8.2 Semi-competing risks data ............................................. 112
8.2.1 Introduction ...................................................... 112
8.2.2 Cumulative incidence quantile regression........................... 113
8.2.3 Marginal quantile regression....................................... 114
8.3 Summary and open problems................................................ 116
9 Instrumental Variable Quantile Regression 119
Victor Chernozhukov, Christian Hansen, and Kaspar Wüthrich
9.1 Introduction ............................................................ 120
9.2 Model overview .......................................................... 121
9.2.1 The instrumental variable quantile regression model................ 121
9.2.2 Conditions for point identification............................... 123
9.2.3 Discussion of the IVQR model..................................... 124
9.2.4 Examples......................................................... . 126
9.2.5 Comparison to other approaches..................................... 128
9.3 Basic estimation and inference approaches ............................... 129
9.3.1 Generalized methods of moments and related approaches ............. 130
9.3.2 Inverse quantile regression...................................... 132
9.3.2.1 A useful interpretation of IQR as a GMM estimator....... 133
9.3.3 Weak identification robust inference............................... 134
9.3.4 Finite-sample inference ........................................... 136
9.4 Advanced inference with high-dimensional X............................... 136
9.4.1 Neyman orthogonal scores........................................... 136
9.4.2 Estimation and inference using orthogonal scores................... 138
9.5 Conclusion .............................................................. 139
10 Local Quantile Treatment Effects 145
Blaise Melly and Kaspar Wüthrich
10.1 Introduction ............................................................ 145
10.2 Framework, estimands and identification ................................ 148
10.2.1 Without covariates................................................ 148
10.2.2 In the presence of covariates: conditional LQTE................... 151
10.2.3 In the presence of covariates: unconditional LQTE................. 152
10.3 Estimation and inference ................................................ 154
10.4 Extensions .............................................................. 155
10.4.1 Regression discontinuity design................................... 155
10.4.2 Multi-valued and continuous instruments........................... 156
10.4.3 Testing instrument validity....................................... 157
10.5 Comparison to the instrumental variable quantile regression model........ 158
10.6 Conclusion and open problems............................................ 160
Contents
xii
11 Quantile Regression with Measurement Errors and Missing Data 165
Ying Wei
11.1 Introduction ........................................................... 165
11.2 Quantile regression with measurement errors ............................ 166
11.2.1 Linear quantile regression with measurement errors............... 166
11.2.1.1 Semiparametric joint estimating equations................. 166
11.2.1.2 Other methods for linear quantile regression with measure-
ment errors....................................................... 169
11.2.2 Nonparametric and semiparametric quantile regression model with
measurement errors .............................................. 171
11.3 Quantile regression with missing data..................................... 172
11.3.1 Statistical methods handling missing covariates in quantile regression 173
11.3.1.1 Multiple imputation algorithm............................. 173
11.3.1.2 Modified MI algorithms.................................... 175
11.3.1.3 EM algorithm.............................................. 177
11.3.1.4 IPW algorithms............................................ 178
11.3.2 Statistical methods handling missing outcomes in quantile regression 178
11.3.2.1 Imputation approaches for missing outcomes................ 178
11.3.2.2 Statistical methods for longitudinal dropout ............. 180
12 Multiple-Output Quantile Regression 185
Marc Hallin and Miroslav Siman
12.1 Multivariate quantiles, and the ordering of Md, 2 ................... 185
12.2 Directional approaches ................................................... 187
12.2.1 Projection methods ................................................ 187
12.2.1.1 Marginal (coordinatewise) quantiles....................... 187
12.2.1.2 Quantile biplots.......................................... 187
12.2.1.3 Directional quantile hyperplanes and contours............. 188
12.2.1.4 Relation to halfspace depth............................... 189
12.2.2 Directional Koenker-Bassett methods................................ 189
12.2.2.1 Location case (p = 0)..................................... 189
12.2.2.2 (Nonparametric) regression case (p ^ 1) 191
12.3 Direct approaches ........................................................ 193
12.3.1 Spatial (geometric) quantile methods............................... 195
12.3.1.1 A spatial check function.................................. 195
12.3.1.2 Linear spatial quantile regression........................ 196
12.3.1.3 Nonparametric spatial quantile regression................. 197
12.3.2 Elliptical quantiles............................................... 197
12.3.2.1 Location case............................................. 197
12.3.2.2 Linear regression case.................................... 198
12.3.3 Depth-based quantiles.............................................. 200
12.3.3.1 Halfspace depth quantiles................................. 200
12.3.3.2 Monge-Kantorovich quantiles............................... 201
12.4 Some other concepts, and applications..................................... 203
12.5 Conclusion ............................................................... 204
13 Sample Selection in Quantile Regression: A Survey 209
Manuel Arellano and Stephane Bonhomme
13.1 Introduction ............................................................. 209
13.2 Heckman’s parametric selection model...................................... 211
13.2.1 Two-step estimation in Gaussian models............................. 212
Contents xiii
13.3 A quantile generalization ............................................... 212
13.3.1 A quantile selection model........................................ 212
13.3.2 Estimation........................................................ 213
13.4 Identification........................................................... 216
13.5 Other approaches ........................................................ 216
13.5.1 A likelihood approach............................................. 217
13.5.2 Control function approaches....................................... 217
13.5.3 Link to censoring corrections..................................... 217
13.6 Empirical illustration .................................................. 218
13.7 Conclusion .............................................................. 221
14 Nonparametric Quantile Regression for Banach-Valued Response 225
Joydeep Chowdhury and Probal Chaudhuri
14.1 Introduction ............................................................ 225
14.2 Regression quantiles in Banach spaces.................................... 229
14.3 Nonparametric estimation ................................................ 231
14.4 Data analysis.......................................................... 232
14.4.1 Simulation ....................................................... 232
14.4.2 Tecator data...................................................... 234
14.4.3 Pediatric airway data............................................ 234
14.4.4 Cigarette data . ............................................... 237
14.4.4.1 Regression of price curve on sales curve.................. 237
14.5 Consistency ............................................................. 240
14.5.1 Additional mathematical details ........................... 245
14.6 Concluding remarks..................................................... 249
15 High-Dimensional Quantile Regression 253
Alexandre Belloni, Victor Chernozhukov, and Kengo Kato
15.1 Introduction ............................................................ 253
15.2 Estimation of the conditional quantile function.......................... 256
15.2.1 Regularity conditions ............................................ 256
15.2.2 ¿i-penalized quantile regression.................................. 257
15.2.3 Refitted quantile regression after selection...................... 259
15.2.4 Group lasso for quantile regression models........................ 260
15.2.5 Estimation of the conditional density............................. 261
15.3 Confidence bands for the coefficient process............................ 261
15.3.1 Construction of an orthogonal score function...................... 263
15.3.2 Regularity conditions ............................................ 265
15.3.3 Score function estimator.......................................... 266
15.3.4 Double selection estimator........................................ 267
15.3.5 Confidence bands.................................................. 267
15.3.6 Confidence bands via inverse statistics........................... 269
16 Nonconvex Penalized Quantile Regression: A Review of Methods, Theory
and Algorithms 273
Lan Wang
16.1 Introduction .......................................................... 273
16.2 High-dimensional sparse linear quantile regression .................. 275
16.2.1 Background on penalized high-dimensional regression and the choice
of penalty function............................................. 275
16.2.2 Nonconvex penalized high-dimensional linear quantile regression . . 276
XIV
Contents
16.2.2.1 Overview.................................................. 276
16.2.2.2 Oracle property of the nonconvex penalized quantile regres-
sion estimator.................................................... 278
16.3 High-dimensional sparse semiparametric quantile regression............... 279
16.3.1 Overview.......................................................... 279
16.3.2 Nonconvex penalized partially linear additive quantile regression . . 279
16.3.3 Oracle properties................................................. 280
16.4 Computational aspects of nonconvex penalized quantile regression......... 281
16.4.1 Linear programming based algorithms (moderately large p).......... 281
16.4.2 New iterative coordinate descent algorithm (larger p)............. 282
16.5 Other related problems .................................................. 283
16.5.1 Simultaneous estimation and variable selection at multiple quantiles 283
16.5.2 Two-stage analysis with quantile-adaptive screening.................... 284
16.5.2.1 Background..................................................... 284
16.5.2.2 Quantile-adaptive model-free nonlinear screening............... 284
16.6 Discussion ................................................................... 285
17 QAR and Quantile Time Series Analysis 293
Zhijie Xiao
17.1 Introduction ................................................................. 293
17.2 Quantile regression estimation of traditional time series models......... 294
17.2.1 Quantile regression estimation of the traditional AR model............. 295
17.2.2 Quantile regressions of other time series models with i.i.d. errors . . 296
17.2.3 Quantile regression estimation of ARMA models.......................... 297
17.2.4 Quantile regressions with serially correlated errors................... 298
17.3 Quantile regressions with ARCH/GARCH errors................................... 299
17.4 Quantile regressions with heavy-tailed errors ........................... 306
17.5 Quantile regression for nonstationary time series........................ 307
17.5.1 Quantile regression for trending time series........................... 307
17.5.2 Unit-root quantile regressions......................................... 308
17.5.3 Quantile regression on cointegrated time series........................ 310
17.6 The QAR process .............................................................. 312
17.6.1 The linear QAR process................................................. 313
17.6.2 Nonlinear QAR models................................................... 317
17.6.3 Quantile autoregression based on transformations....................... 319
17.7 Other dynamic quantile models ................................................ 320
17.8 Quantile spectral analysis.................................................. 322
17.8.1 Quantile cross-covariances and quantile spectrum....................... 323
17.8.2 Quantile periodograms.................................................. 324
17.8.3 Relationship to quantile regression on harmonic regressors............. 325
17.8.4 Estimation of quantile spectral density................................ 327
17.9 Quantile regression based forecasting ........................................ 328
17.10Conclusion ................................................................... 329
18 Extremal Quantile Regression 333
Victor Chernozhukov, Ivan Fernandez- Val, and Tetsuya Kaji
18.1 Introduction ................................................................. 334
18.2 Extreme quantile models ...................................................... 336
18.2.1 Pareto-type and regularly varying tails................................ 336
18.2.2 Extremal quantile regression models.................................... 337
18.3 Estimation and inference methods.............................................. 338
Contents
XV
18.3.1 Sampling conditions................................................ 338
18.3.2 Univariave case: Marginal quantiles................................ 338
18.3.2.1 Extreme order approximation................................ 339
18.3.2.2 Intermediate order approximation .......................... 339
18.3.2.3 Estimation of £ 340
18.3.2.4 Estimation of At .......................................... 341
18.3.2.5 Computing quantiles of the limit extreme value distributions 342
18.3.2.6 Median bias correction and confidence intervals............ 343
18.3.2.7 Extrapolation estimator for very extremes ................. 344
18.3.3 Multivariate case: Conditional quantiles......................... 344
18.3.3.1 Extreme order approximation................................ 345
18.3.3.2 Intermediate order approximation........................... 345
18.3.3.3 Estimation of f and 7...................................... 346
18.3.3.4 Estimation of At .......................................... 346
18.3.3.5 Computing quantiles of the limit extreme value distributions 347
18.3.3.6 Median bias correction and confidence intervals............ 349
18.3.3.7 Extrapolation estimator for very extremes ................. 349
18.3.4 Extreme value versus normal inference.............................. 350
18.4 Empirical applications.................................................... 350
18.4.1 Value-at-risk prediction........................................... 351
18.4.2 Contagion of financial risk........................................ 354
19 Quantile Regression Methods for Longitudinal Data 363
Antonio F. Galvao and Kengo Kato
19.1 Introduction ............................................................. 363
19.2 Panel quantile regression model .......................................... 365
19.3 Fixed effects estimation................................................. 366
19.3.1 FE-QR estimator.................................................... 366
19.3.2 FE-SQR estimator................................................... 368
19.3.2.1 Bias correction: Analytical method......................... 369
19.3.2.2 Bias correction: Jackknife................................. 370
19.3.3 Alternative FE approaches ......................................... 371
19.3.3.1 Shrinkage.................................................. 371
19.3.3.2 Minimum distance........................................... 371
19.3.3.3 Two-step estimation of Canay (2011)........................ 372
19.4 Correlated random effects................................................. 373
19.5 Extensions ............................................................... 374
19.5.1 Endogeneity........................................................ 374
19.5.2 Censoring.......................................................... 374
19.5.3 Group-level treatments............................................. 376
19.5.4 Semiparametric QR for longitudinal data............................ 377
19.6 Conclusion ............................................................... 378
20 Quantile Regression Applications in Finance 381
Oliver Linton and Zhijie Xiao
20.1 Introduction ............................................................. 381
20.2 Quantile regression in risk management ................................... 383
20.2.1 Value-at-risk..................................................... 383
20.2.2 Expected shortfall................................................. 388
20.3 Upper quantile information and financial markets ........................ 391
20.4 Quantile regression and portfolio allocation.............................. 393
XVI
Contents
20.4.1 The mean-ES portfolio construction................................ 394
20.4.2 The multi-quantile portfolio construction.......................... 395
20.5 Stochastic dominance and quantile regression.............................. 397
20.6 Quantile dependence ...................................................... 399
20.6.1 Directional predictability via the quantilogram................... 400
20.6.2 Causality in quantiles............................................. 402
20.7 Concluding remarks........................................................ 403
21 Quantile Regression for Genetic and Genomic Applications 409
Laurent Briollais and Gilles Durrieu
21.1 Introduction ............................................................. 409
21.2 Genetic applications...................................................... 410
21.2.1 Background and definitions......................................... 410
21.2.2 Candidate gene association study of child BMI..................... 411
21.2.3 GWAS of birthweight................................................ 412
21.2.4 Genetic association with a set of markers......................... 414
21.3 Genomic and other -omic applications...................................... 415
21.3.1 Background......................................................... 415
21.3.2 Genomic data pre-processing........................................ 416
21.3.3 Sample size determination in gene expression studies.............. 417
21.3.4 Determination of chromosomal region aberrations.................... 419
21.3.5 Robust estimation and outlier determination in genomics........... 420
21.3.6 Genomic analysis of set of genes.................................. 422
21.4 Conclusion................................................................ 423
22 Quantile Regression Applications in Ecology and the Environmental Sci-
ences 429
Brian S. Cade
22.1 Introduction ...................................................... 429
22.2 Water quality trends over time............................................ 431
22.2.1 A single site within a watershed .................................. 432
22.2.2 Multiple sites within a watershed.................................. 436
22.2.3 Estimation with below-detection limit values in a single site within a
watershed.......................................................... 436
22.2.4 Additional extensions possible for water quality and flow trend anal-
yses ..................................................................... 439
22.3 Herbaceous plant species diversity and atmospheric nitrogen deposition . . 442
22.3.1 Quantile regression estimates..................................... 444
22.3.2 Partial effects of nitrogen deposition and pH and critical loads . . . 444
22.3.3 Additional possible refinements to the model....................... 449
22.4 Discussion ............................................................... 449
Index
455
|
| any_adam_object | 1 |
| author2 | Koenker, Roger 1947- Chernozhukov, Victor He, Xuming ca. 20/21. Jahrhundert Peng, Limin |
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| author2_variant | r k rk v c vc x h xh l p lp |
| author_GND | (DE-588)131874632 (DE-588)129354759 (DE-588)170895238 (DE-588)136267823 |
| author_facet | Koenker, Roger 1947- Chernozhukov, Victor He, Xuming ca. 20/21. Jahrhundert Peng, Limin |
| building | Verbundindex |
| bvnumber | BV044509242 |
| classification_rvk | QH 234 |
| ctrlnum | (OCoLC)999726158 (DE-599)GBV881112925 |
| discipline | Wirtschaftswissenschaften |
| format | Book |
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| genre | (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV044509242 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T18:04:43Z |
| institution | BVB |
| isbn | 9781498725286 |
| language | English |
| lccn | 2017005283 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029909072 |
| oclc_num | 999726158 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-739 DE-523 DE-N2 DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-739 DE-523 DE-N2 DE-20 |
| physical | xix, 463 Seiten Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Handbooks of modern statistical methods |
| spellingShingle | Handbook of quantile regression Quantile regression Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Quantil (DE-588)4224812-7 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4224812-7 (DE-588)4143413-4 |
| title | Handbook of quantile regression |
| title_auth | Handbook of quantile regression |
| title_exact_search | Handbook of quantile regression |
| title_full | Handbook of quantile regression edited by Roger Koenker, Victor Chernozhukov, Xuming He, Limin Peng |
| title_fullStr | Handbook of quantile regression edited by Roger Koenker, Victor Chernozhukov, Xuming He, Limin Peng |
| title_full_unstemmed | Handbook of quantile regression edited by Roger Koenker, Victor Chernozhukov, Xuming He, Limin Peng |
| title_short | Handbook of quantile regression |
| title_sort | handbook of quantile regression |
| topic | Quantile regression Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Quantil (DE-588)4224812-7 gnd |
| topic_facet | Quantile regression Regression analysis Regressionsanalyse Quantil Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029909072&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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