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Handbook of Quantile Regression [Hardback]

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  • Formāts: Hardback, 484 pages, height x width: 254x178 mm, weight: 1068 g, 12 Tables, black and white; 74 Line drawings, black and white; 32 Halftones, black and white; 106 Illustrations, black and white
  • Sērija : Chapman & Hall/CRC Handbooks of Modern Statistical Methods
  • Izdošanas datums: 25-Oct-2017
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1498725287
  • ISBN-13: 9781498725286
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Handbook of Quantile RegressionPalielināt
  • Formāts: Hardback, 484 pages, height x width: 254x178 mm, weight: 1068 g, 12 Tables, black and white; 74 Line drawings, black and white; 32 Halftones, black and white; 106 Illustrations, black and white
  • Sērija : Chapman & Hall/CRC Handbooks of Modern Statistical Methods
  • Izdošanas datums: 25-Oct-2017
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1498725287
  • ISBN-13: 9781498725286
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781498725286.html
Keywords:

Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss.

Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments.

The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings.

The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.

Recenzijas

"Given the substantial impact that Quantile Regression (QR) has had in the statistical literature in general (and particularly in econometrics), a handbook that acknowledges this impact and explores its breadth is especially welcome. This volume provides an excellent coverage of the developments in, and applications of, QR over the past 40 years. A brief historical "memoir" by Bassett and Koenker is followed by 21 chapters contributed by a broad cross-section of scholars, all of whom are experts in QR. These chapters amply illustrate the versatility of QR, and the wide range of variations on its central theme that can be developed to give us a powerful suite of inferential methodsThis Handbook is a wonderful resource for graduate students and researchers alike. As has been noted already, the various contributions provide an excellent coverage of the use of QR in the context of a variety of statistical models and types of data. In addition, the book provides illustrations of the application of QR in finance, ecology and environmental sciences, and in genetic and genomic studies. The editors and contributors are to be congratulated on assembling this valuable handbook, which will serve to update and significantly extend our understanding of the richness of QR methods." David E. Giles in Statistical Papers, September 2018

"Quantile regression was introduced in 1757 but not perfected until Koenker and Bassett made it a modern tool for robust analyses in linear models in 1978. This book is testimony to its continuing vitality and growing relevance in the big data era." Stephen M. Stigler, Ernest DeWitt Burton Distinguished Service Professor of Statistics, University of Chicago

"Since its invention by Koenker and Bassett, quantile regression has moved from intriguing statistical curiosity to a central empirical tool in the applied econometrician's toolkit. This volume offers a valuable, accessible, and timely summary of the many major methodological developments that have expanded and enriched our understanding of quantile regression and its many applications. Many of the volume's contributors have been active in promoting the "quantile revolution." Practitioners and methodologists alike should find the essays in this Handbook useful and interesting." Josh Angrist, MIT Department of Economics

"Quantile regression is a generalization of median regression. It is not the usual sum of squares of residuals that is minimized, but the sum of their absolute values. Median regression is known for its robustness. In 1978 Koenker and Basset published a paper in Econometrica in which they introduced regression quantiles. I have access to eight other handbooks in the CRC series, and this one is by far the most theoretical, with a very high formula density. In places it looks like a handbook of the theory of quantile regression. Under such an umbrella, there is a lot of value to be found (see the table of contents on the publishers website). There are many references at the end of the various chapters, which indicates the popularity of quantile regression. They are a good source for further study." -Paul Eilers, ISCB June 2018

Preface xvii
Contributors xix
Introduction 1(2)
1 A Quantile Regression Memoir 3(4)
Gilbert W. Bassett Jr
Roger Koenker
1.1 Long ago
3(4)
2 Resampling Methods 7(14)
Xuming He
2.1 Introduction
7(1)
2.2 Paired bootstrap
8(1)
2.3 Residual-based bootstrap
9(2)
2.4 Generalized bootstrap
11(1)
2.5 Estimating function bootstrap
11(1)
2.6 Markov chain marginal bootstrap
12(1)
2.7 Resampling methods for clustered data
13(1)
2.8 Resampling methods for censored quantile regression
14(1)
2.9 Bootstrap for post-model selection inference
15(6)
3 Quantile Regression: Penalized 21(20)
Ivan Mizera
3.1 Penalized: how?
21(2)
3.1.1 A probability path
21(1)
3.1.2 Regularization of ill-posed problems
22(1)
3.2 Penalized: what?
23(8)
3.2.1 The finite differences of Whittaker and others
23(1)
3.2.2 Functions and their derivatives
24(2)
3.2.3 Quantile regression with smoothing splines
26(2)
3.2.4 Quantile smoothing splines
28(1)
3.2.5 Total-variation splines
29(2)
3.3 Penalized: what else?
31(10)
3.3.1 Tuning
31(1)
3.3.2 Multiple covariates
32(2)
3.3.3 Additive fits, confidence bandaids, and other phantasmagorias
34(7)
4 Bayesian Quantile Regression 41(14)
Huixia Judy Wang
Yunwen Yang
4.1 Introduction
41(1)
4.2 Asymmetric Laplace likelihood
42(3)
4.3 Empirical likelihood
45(2)
4.4 Nonparametric and semiparametric likelihoods
47(4)
4.4.1 Mixture-type likelihood
47(2)
4.4.2 Approximate likelihood via quantile process
49(2)
4.5 Discussion
51(4)
5 Computational Methods for Quantile Regression 55(14)
Roger Koenker
5.1 Introduction
55(2)
5.2 Exterior point methods
57(1)
5.3 Interior point methods
58(2)
5.4 Preprocessing
60(1)
5.5 First-order, proximal methods
61(8)
5.5.1 Proximal operators and the Moreau envelope
61(3)
5.5.2 Alternating direction method of multipliers
64(1)
5.5.3 Proximal performance
65(4)
6 Survival Analysis: A Quantile Perspective 69(20)
Zhiliang Ying
Tony Sit
6.1 Introduction
69(3)
6.1.1 Notation
70(1)
6.1.2 Censoring
71(1)
6.2 Important models
72(7)
6.2.1 Parametric models
72(1)
6.2.2 Nonparametric estimators
73(2)
6.2.2.1 Kaplan-Meier estimator
73(2)
6.2.2.2 Nelson-Aalen estimator
75(1)
6.2.3 Regression models
75(4)
6.2.3.1 Cox proportional hazards model
75(1)
6.2.3.2 Accelerated failure time model
76(2)
6.2.3.3 Aalen additive hazard model
78(1)
6.3 Quantile estimation based on censored data
79(10)
6.3.1 Quantile estimation
79(1)
6.3.2 Median and quantile regression
80(2)
6.3.3 Discussion and miscellanea
82(7)
7 Quantile Regression for Survival Analysis 89(16)
Limin Peng
7.1 Introduction
89(1)
7.2 Quantile regression for randomly censored data
90(7)
7.2.1 Random right censoring with C always known
90(1)
7.2.2 Covariate-independent random right censoring
91(1)
7.2.3 Standard random right censoring
92(3)
7.2.3.1 Approaches based on the principle of self-consistency
92(1)
7.2.3.2 Martingale-based approach
93(1)
7.2.3.3 Locally weighted method
94(1)
7.2.4 Variance estimation and other inference
95(2)
7.2.4.1 Variance estimation
95(1)
7.2.4.2 Second-stage inference
96(1)
7.2.4.3 Model checking
96(1)
7.3 Quantile regression in other survival settings
97(1)
7.3.1 Known random left censoring and/or left truncation
97(1)
7.3.2 Censored data with a survival cure fraction
98(1)
7.4 An illustration of quantile regression for survival analysis
98(7)
8 Survival Analysis with Competing Risks and Semi-competing Risks Data 105(14)
Ruosha Li
Limin Peng
8.1 Competing risks data
105(7)
8.1.1 Introduction
105(1)
8.1.2 Cumulative incidence quantile regression
106(2)
8.1.3 Data analysis example
108(2)
8.1.4 Marginal quantile regression
110(2)
8.2 Semi-competing risks data
112(4)
8.2.1 Introduction
112(1)
8.2.2 Cumulative incidence quantile regression
113(1)
8.2.3 Marginal quantile regression
114(2)
8.3 Summary and open problems
116(3)
9 Instrumental Variable Quantile Regression 119(26)
Victor Chernozhukov
Christian Hansen
Kaspar Wuthrich
9.1 Introduction
120(1)
9.2 Model overview
121(8)
9.2.1 The instrumental variable quantile regression model
121(2)
9.2.2 Conditions for point identification
123(1)
9.2.3 Discussion of the IVQR model
124(2)
9.2.4 Examples
126(2)
9.2.5 Comparison to other approaches
128(1)
9.3 Basic estimation and inference approaches
129(7)
9.3.1 Generalized methods of moments and related approaches
130(2)
9.3.2 Inverse quantile regression
132(2)
9.3.2.1 A useful interpretation of IQR as a GMM estimator
133(1)
9.3.3 Weak identification robust inference
134(2)
9.3.4 Finite-sample inference
136(1)
9.4 Advanced inference with high-dimensional X
136(3)
9.4.1 Neyman orthogonal scores
136(2)
9.4.2 Estimation and inference using orthogonal scores
138(1)
9.5 Conclusion
139(6)
10 Local Quantile Treatment Effects 145(20)
Blaise Melly
Kaspar Wuthrich
10.1 Introduction
145(3)
10.2 Framework, estimands and identification
148(6)
10.2.1 Without covariates
148(3)
10.2.2 In the presence of covariates: conditional LQTE
151(1)
10.2.3 In the presence of covariates: unconditional LQTE
152(2)
10.3 Estimation and inference
154(1)
10.4 Extensions
155(3)
10.4.1 Regression discontinuity design
155(1)
10.4.2 Multi-valued and continuous instruments
156(1)
10.4.3 Testing instrument validity
157(1)
10.5 Comparison to the instrumental variable quantile regression model
158(2)
10.6 Conclusion and open problems
160(5)
11 Quantile Regression with Measurement Errors and Missing Data 165(20)
Ying Wei
11.1 Introduction
165(1)
11.2 Quantile regression with measurement errors
166(6)
11.2.1 Linear quantile regression with measurement errors
166(5)
11.2.1.1 Semiparametric joint estimating equations
166(3)
11.2.1.2 Other methods for linear quantile regression with measurement errors
169(2)
11.2.2 Nonparametric and semiparametric quantile regression model with measurement errors
171(1)
11.3 Quantile regression with missing data
172(13)
11.3.1 Statistical methods handling missing covariates in quantile regression
173(5)
11.3.1.1 Multiple imputation algorithm
173(2)
11.3.1.2 Modified MI algorithms
175(2)
11.3.1.3 EM algorithm
177(1)
11.3.1.4 IPW algorithms
178(1)
11.3.2 Statistical methods handling missing outcomes in quantile regression
178(9)
11.3.2.1 Imputation approaches for missing outcomes
178(2)
11.3.2.2 Statistical methods for longitudinal dropout
180(5)
12 Multiple-Output Quantile Regression 185(24)
Marc Hallin
Miroslav Siman
12.1 Multivariate quantiles, and the ordering of Rd, d > or = to 2
185(2)
12.2 Directional approaches
187(6)
12.2.1 Projection methods
187(2)
12.2.1.1 Marginal (coordinatewise) quantiles
187(1)
12.2.1.2 Quantile biplots
187(1)
12.2.1.3 Directional quantile hyperplanes and contours
188(1)
12.2.1.4 Relation to halfspace depth
189(1)
12.2.2 Directional Koenker-Bassett methods
189(4)
12.2.2.1 Location case (p = 0)
189(2)
12.2.2.2 (Nonparametric) regression case (p > or = to 1)
191(2)
12.3 Direct approaches
193(10)
12.3.1 Spatial (geometric) quantile methods
195(2)
12.3.1.1 A spatial check function
195(1)
12.3.1.2 Linear spatial quantile regression
196(1)
12.3.1.3 Nonparametric spatial quantile regression
197(1)
12.3.2 Elliptical quantiles
197(3)
12.3.2.1 Location case
197(1)
12.3.2.2 Linear regression case
198(2)
12.3.3 Depth-based quantiles
200(11)
12.3.3.1 Halfspace depth quantiles
200(1)
12.3.3.2 Monge-Kantorovich quantiles
201(2)
12.4 Some other concepts, and applications
203(1)
12.5 Conclusion
204(5)
13 Sample Selection in Quantile Regression: A Survey 209(16)
Manuel Arellano
Stephane Bonhomme
13.1 Introduction
209(2)
13.2 Heckman's parametric selection model
211(1)
13.2.1 Two-step estimation in Gaussian models
212(1)
13.3 A quantile generalization
212(4)
13.3.1 A quantile selection model
212(1)
13.3.2 Estimation
213(3)
13.4 Identification
216(1)
13.5 Other approaches
216(2)
13.5.1 A likelihood approach
217(1)
13.5.2 Control function approaches
217(1)
13.5.3 Link to censoring corrections
217(1)
13.6 Empirical illustration
218(3)
13.7 Conclusion
221(4)
14 Nonparametric Quantile Regression for Banach-Valued Response 225(28)
Joydeep Chowdhury
Probal Chaudhuri
14.1 Introduction
225(4)
14.2 Regression quantiles in Banach spaces
229(2)
14.3 Nonparametric estimation
231(1)
14.4 Data analysis
232(8)
14.4.1 Simulation
232(2)
14.4.2 Tecator data
234(1)
14.4.3 Pediatric airway data
234(3)
14.4.4 Cigarette data
237(3)
14.4.4.1 Regression of price curve on sales curve
237(3)
14.5 Consistency
240(9)
14.5.1 Additional mathematical details
245(4)
14.6 Concluding remarks
249(4)
15 High-Dimensional Quantile Regression 253(20)
Alexandre Belloni
Victor Chernozhukov
Kengo Kato
15.1 Introduction
253(3)
15.2 Estimation of the conditional quantile function
256(5)
15.2.1 Regularity conditions
256(1)
15.2.2 Li-penalized quantile regression
257(2)
15.2.3 Refitted quantile regression after selection
259(1)
15.2.4 Group lasso for quantile regression models
260(1)
15.2.5 Estimation of the conditional density
261(1)
15.3 Confidence bands for the coefficient process
261(12)
15.3.1 Construction of an orthogonal score function
263(2)
15.3.2 Regularity conditions
265(1)
15.3.3 Score function estimator
266(1)
15.3.4 Double selection estimator
267(1)
15.3.5 Confidence bands
267(2)
15.3.6 Confidence bands via inverse statistics
269(4)
16 Nonconvex Penalized Quantile Regression: A Review of Methods, Theory and Algorithms 273(20)
Lan Wang
16.1 Introduction
273(2)
16.2 High-dimensional sparse linear quantile regression
275(4)
16.2.1 Background on penalized high-dimensional regression and the choice of penalty function
275(1)
16.2.2 Nonconvex penalized high-dimensional linear quantile regression
276(3)
16.2.2.1 Overview
276(2)
16.2.2.2 Oracle property of the nonconvex penalized quantile regression estimator
278(1)
16.3 High-dimensional sparse semiparametric quantile regression
279(2)
16.3.1 Overview
279(1)
16.3.2 Nonconvex penalized partially linear additive quantile regression
279(1)
16.3.3 Oracle properties
280(1)
16.4 Computational aspects of nonconvex penalized quantile regression
281(2)
16.4.1 Linear programming based algorithms (moderately large p)
281(1)
16.4.2 New iterative coordinate descent algorithm (larger p)
282(1)
16.5 Other related problems
283(2)
16.5.1 Simultaneous estimation and variable selection at multiple quintiles
283(1)
16.5.2 Two-stage analysis with quantile-adaptive screening
284(10)
16.5.2.1 Background
284(1)
16.5.2.2 Quantile-adaptive model-free nonlinear screening
284(1)
16.6 Discussion
285(8)
17 QAR and Quantile Time Series Analysis 293(40)
Zhijie Xiao
17.1 Introduction
293(1)
17.2 Quantile regression estimation of traditional time series models
294(5)
17.2.1 Quantile regression estimation of the traditional AR model
295(1)
17.2.2 Quantile regressions of other time series models with i.i.d. errors
296(1)
17.2.3 Quantile regression estimation of ARMA models
297(1)
17.2.4 Quantile regressions with serially correlated errors
298(1)
17.3 Quantile regressions with ARCH/GARCH errors
299(7)
17.4 Quantile regressions with heavy-tailed errors
306(1)
17.5 Quantile regression for nonstationary time series
307(5)
17.5.1 Quantile regression for trending time series
307(1)
17.5.2 Unit-root quantile regressions
308(2)
17.5.3 Quantile regression on cointegrated time series
310(2)
17.6 The QAR process
312(8)
17.6.1 The linear QAR process
313(4)
17.6.2 Nonlinear QAR models
317(2)
17.6.3 Quantile autoregression based on transformations
319(1)
17.7 Other dynamic quantile models
320(2)
17.8 Quantile spectral analysis
322(6)
17.8.1 Quantile cross-covariances and quantile spectrum
323(1)
17.8.2 Quantile periodograms
324(1)
17.8.3 Relationship to quantile regression on harmonic regressors
325(2)
17.8.4 Estimation of quantile spectral density
327(1)
17.9 Quantile regression based forecasting
328(1)
17.10 Conclusion
329(4)
18 Extremal Quantile Regression 333(30)
Victor Chernozhukov
Ivan Fernandez-Val
Tetsuya Kaji
18.1 Introduction
334(2)
18.2 Extreme quantile models
336(2)
18.2.1 Pareto-type and regularly varying tails
336(1)
18.2.2 Extremal quantile regression models
337(1)
18.3 Estimation and inference methods
338(12)
18.3.1 Sampling conditions
338(1)
18.3.2 Univariave case: Marginal quantiles
338(6)
18.3.2.1 Extreme order approximation
339(1)
18.3.2.2 Intermediate order approximation
339(1)
18.3.2.3 Estimation of
340(1)
18.3.2.4 Estimation of AT
341(1)
18.3.2.5 Computing quantiles of the limit extreme value distributions
342(1)
18.3.2.6 Median bias correction and confidence intervals
343(1)
18.3.2.7 Extrapolation estimator for very extremes
344(1)
18.3.3 Multivariate case: Conditional quantiles
344(6)
18.3.3.1 Extreme order approximation
345(1)
18.3.3.2 Intermediate order approximation
345(1)
18.3.3.3 Estimation of and 7
346(1)
18.3.3.4 Estimation of AT
346(1)
18.3.3.5 Computing quantiles of the limit extreme value distributions
347(2)
18.3.3.6 Median bias correction and confidence intervals
349(1)
18.3.3.7 Extrapolation estimator for very extremes
349(1)
18.3.4 Extreme value versus normal inference
350(1)
18.4 Empirical applications
350(13)
18.4.1 Value-at-risk prediction
351(3)
18.4.2 Contagion of financial risk
354(9)
19 Quantile Regression Methods for Longitudinal Data 363(18)
Antonio F. Galvao
Kengo Kato
19.1 Introduction
363(2)
19.2 Panel quantile regression model
365(1)
19.3 Fixed effects estimation
366(7)
19.3.1 FE-QR estimator
366(2)
19.3.2 FE-SQR estimator
368(3)
19.3.2.1 Bias correction: Analytical method
369(1)
19.3.2.2 Bias correction: Jackknife
370(1)
19.3.3 Alternative FE approaches
371(3)
19.3.3.1 Shrinkage
371(1)
19.3.3.2 Minimum distance
371(1)
19.3.3.3 Two-step estimation of Canay (2011)
372(1)
19.4 Correlated random effects
373(1)
19.5 Extensions
374(4)
19.5.1 Endogeneity
374(1)
19.5.2 Censoring
374(2)
19.5.3 Group-level treatments
376(1)
19.5.4 Semiparametric QR for longitudinal data
377(1)
19.6 Conclusion
378(3)
20 Quantile Regression Applications in Finance 381(28)
Oliver Linton
Zhijie Xiao
20.1 Introduction
381(2)
20.2 Quantile regression in risk management
383(8)
20.2.1 Value-at-risk
383(5)
20.2.2 Expected shortfall
388(3)
20.3 Upper quantile information and financial markets
391(2)
20.4 Quantile regression and portfolio allocation
393(4)
20.4.1 The mean-ES portfolio construction
394(1)
20.4.2 The multi-quantile portfolio construction
395(2)
20.5 Stochastic dominance and quantile regression
397(2)
20.6 Quantile dependence
399(4)
20.6.1 Directional predictability via the quantilogram
400(2)
20.6.2 Causality in quantiles
402(1)
20.7 Concluding remarks
403(6)
21 Quantile Regression for Genetic and Genomic Applications 409(20)
Laurent Briollais
Gilles Durrieu
21.1 Introduction
409(1)
21.2 Genetic applications
410(5)
21.2.1 Background and definitions
410(1)
21.2.2 Candidate gene association study of child BMI
411(1)
21.2.3 GWAS of birthweight
412(2)
21.2.4 Genetic association with a set of markers
414(1)
21.3 Genomic and other -omic applications
415(8)
21.3.1 Background
415(1)
21.3.2 Genomic data pre-processing
416(1)
21.3.3 Sample size determination in gene expression studies
417(2)
21.3.4 Determination of chromosomal region aberrations
419(1)
21.3.5 Robust estimation and outlier determination in genomics
420(2)
21.3.6 Genomic analysis of set of genes
422(1)
21.4 Conclusion
423(6)
22 Quantile Regression Applications in Ecology and the Environmental Sciences 429(26)
Brian S. Cade
22.1 Introduction
429(2)
22.2 Water quality trends over time
431(11)
22.2.1 A single site within a watershed
432(4)
22.2.2 Multiple sites within a watershed
436(1)
22.2.3 Estimation with below-detection limit values in a single site within a watershed
436(3)
22.2.4 Additional extensions possible for water quality and flow trend analyses
439(3)
22.3 Herbaceous plant species diversity and atmospheric nitrogen deposition
442(7)
22.3.1 Quantile regression estimates
444(1)
22.3.2 Partial effects of nitrogen deposition and pH and critical loads
444(5)
22.3.3 Additional possible refinements to the model
449(1)
22.4 Discussion
449(6)
Index 455
Roger Koenker, University of Illinois



Victor Chernozhukov, MIT



Xuming He, University of Michigan



Limin Peng, Emory University