Handbook of quantile regression /

Bibliographic Details
Corporate Author:	ProQuest (Firm)
Other Authors:	Koenker, Roger, 1947- (Editor), Chernozhukov, Victor (Editor), He, Xuming (Editor), Peng, Limin (Editor)
Format:	eBook
Language:	English
Published:	Boca Raton, FL : CRC Press, Taylor & Francis Group, [2018]
Series:	Chapman & Hall/CRC handbooks of modern statistical methods.
Subjects:	Quantile regression. Regression analysis. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Machine generated contents note: 1.1.Long ago / Roger Koenker / Gilbert W. Bassett Jr
2.1.Introduction / Xuming He
2.2.Paired bootstrap / Xuming He
2.3.Residual-based bootstrap / Xuming He
2.4.Generalized bootstrap / Xuming He
2.5.Estimating function bootstrap / Xuming He
2.6.Markov chain marginal bootstrap / Xuming He
2.7.Resampling methods for clustered data / Xuming He
2.8.Resampling methods for censored quantile regression / Xuming He
2.9.Bootstrap for post-model selection inference / Xuming He
3.1.Penalized: how? / Ivan Mizera
3.1.1.A probability path / Ivan Mizera
3.1.2.Regularization of ill-posed problems / Ivan Mizera
3.2.Penalized: what? / Ivan Mizera
3.2.1.The finite differences of Whittaker and others / Ivan Mizera
3.2.2.Functions and their derivatives / Ivan Mizera
3.2.3.Quantile regression with smoothing splines / Ivan Mizera
3.2.4.Quantile smoothing splines / Ivan Mizera
Note continued: 3.2.5.Total-variation splines / Ivan Mizera
3.3.Penalized: what else? / Ivan Mizera
3.3.1.Tuning / Ivan Mizera
3.3.2.Multiple covariates / Ivan Mizera
3.3.3.Additive fits, confidence bandaids, and other phantasmagorias / Ivan Mizera
4.1.Introduction / Yunwen Yang / Huixia Judy Wang
4.2.Asymmetric Laplace likelihood / Yunwen Yang / Huixia Judy Wang
4.3.Empirical likelihood / Yunwen Yang / Huixia Judy Wang
4.4.Nonparametric and semiparametric likelihoods / Yunwen Yang / Huixia Judy Wang
4.4.1.Mixture-type likelihood / Yunwen Yang / Huixia Judy Wang
4.4.2.Approximate likelihood via quantile process / Yunwen Yang / Huixia Judy Wang
4.5.Discussion / Yunwen Yang / Huixia Judy Wang
5.1.Introduction / Roger Koenker
5.2.Exterior point methods / Roger Koenker
5.3.Interior point methods / Roger Koenker
5.4.Preprocessing / Roger Koenker
5.5.First-order, proximal methods / Roger Koenker
Note continued: 5.5.1.Proximal operators and the Moreau envelope / Roger Koenker
5.5.2.Alternating direction method of multipliers / Roger Koenker
5.5.3.Proximal performance / Roger Koenker
6.1.Introduction / Tony Sit / Zhiliang Ying
6.1.1.Notation / Tony Sit / Zhiliang Ying
6.1.2.Censoring / Tony Sit / Zhiliang Ying
6.2.Important models / Tony Sit / Zhiliang Ying
6.2.1.Parametric models / Tony Sit / Zhiliang Ying
6.2.2.Nonparametric estimators / Tony Sit / Zhiliang Ying
6.2.2.1.Kaplan-Meier estimator / Tony Sit / Zhiliang Ying
6.2.2.2.Nelson-Aalen estimator / Tony Sit / Zhiliang Ying
6.2.3.Regression models / Zhiliang Ying / Tony Sit
6.2.3.1.Cox proportional hazards model / Tony Sit / Zhiliang Ying
6.2.3.2.Accelerated failure time model / Tony Sit / Zhiliang Ying
6.2.3.3.Aalen additive hazard model / Tony Sit / Zhiliang Ying
6.3.Quantile estimation based on censored data / Tony Sit / Zhiliang Ying
Note continued: 6.3.1.Quantile estimation / Tony Sit / Zhiliang Ying
6.3.2.Median and quantile regression / Tony Sit / Zhiliang Ying
6.3.3.Discussion and miscellanea / Tony Sit / Zhiliang Ying
7.1.Introduction / Limin Peng
7.2.Quantile regression for randomly censored data / Limin Peng
7.2.1.Random right censoring with C always known / Limin Peng
7.2.2.Covariate-independent random right censoring / Limin Peng
7.2.3.Standard random right censoring / Limin Peng
7.2.3.1.Approaches based on the principle of self-consistency / Limin Peng
7.2.3.2.Martingale-based approach / Limin Peng
7.2.3.3.Locally weighted method / Limin Peng
7.2.4.Variance estimation and other inference / Limin Peng
7.2.4.1.Variance estimation / Limin Peng
7.2.4.2.Second-stage inference / Limin Peng
7.2.4.3.Model checking / Limin Peng
7.3.Quantile regression in other survival settings / Limin Peng
Note continued: 7.3.1.Known random left censoring and/or left truncation / Limin Peng
7.3.2.Censored data with a survival cure fraction / Limin Peng
7.4.An illustration of quantile regression for survival analysis / Limin Peng
8.1.Competing risks data / Limin Peng / Ruosha Li
8.1.1.Introduction / Limin Peng / Ruosha Li
8.1.2.Cumulative incidence quantile regression / Limin Peng / Ruosha Li
8.1.3.Data analysis example / Limin Peng / Ruosha Li
8.1.4.Marginal quantile regression / Limin Peng / Ruosha Li
8.2.Semi-competing risks data / Limin Peng / Ruosha Li
8.2.1.Introduction / Limin Peng / Ruosha Li
8.2.2.Cumulative incidence quantile regression / Limin Peng / Ruosha Li
8.2.3.Marginal quantile regression / Limin Peng / Ruosha Li
8.3.Summary and open problems / Limin Peng / Ruosha Li
9.1.Introduction / Victor Chernozhukov / Kaspar Wuthrich / Christian Hansen
Note continued: 9.2.Model overview / Victor Chernozhukov / Kaspar Wuthrich / Christian Hansen
9.2.1.The instrumental variable quantile regression model / Victor Chernozhukov / Kaspar Wuthrich / Christian Hansen
9.2.2.Conditions for point identification / Victor Chernozhukov / Kaspar Wuthrich / Christian Hansen
9.2.3.Discussion of the IVQR model / Victor Chernozhukov / Kaspar Wuthrich / Christian Hansen
9.2.4.Examples / Victor Chernozhukov / Kaspar Wuthrich / Christian Hansen
9.2.5.Comparison to other approaches / Victor Chernozhukov / Kaspar Wuthrich / Christian Hansen
9.3.Basic estimation and inference approaches / Victor Chernozhukov / Christian Hansen / Kaspar Wuthrich
9.3.1.Generalized methods of moments and related approaches / Victor Chernozhukov / Christian Hansen / Kaspar Wuthrich
9.3.2.Inverse quantile regression / Victor Chernozhukov / Christian Hansen / Kaspar Wuthrich
Note continued: 9.3.2.1.A useful interpretation of IQR as a GMM estimator / Victor Chernozhukov / Christian Hansen / Kaspar Wuthrich
9.3.3.Weak identification robust inference / Victor Chernozhukov / Christian Hansen / Kaspar Wuthrich
9.3.4.Finite-sample inference / Victor Chernozhukov / Christian Hansen / Kaspar Wuthrich
9.4.Advanced inference with high-dimensional X / Victor Chernozhukov / Christian Hansen / Kaspar Wuthrich
9.4.1.Neyman orthogonal scores / Victor Chernozhukov / Christian Hansen / Kaspar Wuthrich
9.4.2.Estimation and inference using orthogonal scores / Victor Chernozhukov / Christian Hansen / Kaspar Wuthrich
9.5.Conclusion / Victor Chernozhukov / Christian Hansen / Kaspar Wuthrich
10.1.Introduction / Blaise Melly / Kaspar Wuthrich
10.2.Framework, estimands and identification / Blaise Melly / Kaspar Wuthrich
10.2.1.Without covariates / Blaise Melly / Kaspar Wuthrich
Note continued: 10.2.2.In the presence of covariates: conditional LQTE / Blaise Melly / Kaspar Wuthrich
10.2.3.In the presence of covariates: unconditional LQTE / Blaise Melly / Kaspar Wuthrich
10.3.Estimation and inference / Blaise Melly / Kaspar Wuthrich
10.4.Extensions / Blaise Melly / Kaspar Wuthrich
10.4.1.Regression discontinuity design / Blaise Melly / Kaspar Wuthrich
10.4.2.Multi-valued and continuous instruments / Blaise Melly / Kaspar Wuthrich
10.4.3.Testing instrument validity / Blaise Melly / Kaspar Wuthrich
10.5.Comparison to the instrumental variable quantile regression model / Blaise Melly / Kaspar Wuthrich
10.6.Conclusion and open problems / Blaise Melly / Kaspar Wuthrich
11.1.Introduction / Ying Wei
11.2.Quantile regression with measurement errors / Ying Wei
11.2.1.Linear quantile regression with measurement errors / Ying Wei
11.2.1.1.Semiparametric joint estimating equations / Ying Wei
Note continued: 11.2.1.2.Other methods for linear quantile regression with measurement errors / Ying Wei
11.2.2.Nonparametric and semiparametric quantile regression model with measurement errors / Ying Wei
11.3.Quantile regression with missing data / Ying Wei
11.3.1.Statistical methods handling missing covariates in quantile regression / Ying Wei
11.3.1.1.Multiple imputation algorithm / Ying Wei
11.3.1.2.Modified MI algorithms / Ying Wei
11.3.1.3.EM algorithm / Ying Wei
11.3.1.4.IPW algorithms / Ying Wei
11.3.2.Statistical methods handling missing outcomes in quantile regression / Ying Wei
11.3.2.1.Imputation approaches for missing outcomes / Ying Wei
11.3.2.2.Statistical methods for longitudinal dropout / Ying Wei
12.1.Multivariate quantiles, and the ordering of Rd, d > or = to 2 / Marc Hallin / Miroslav Siman
12.2.Directional approaches / Marc Hallin / Miroslav Siman
12.2.1.Projection methods / Marc Hallin / Miroslav Siman
Note continued: 12.2.1.1.Marginal (coordinatewise) quantiles / Marc Hallin / Miroslav Siman
12.2.1.2.Quantile biplots / Marc Hallin / Miroslav Siman
12.2.1.3.Directional quantile hyperplanes and contours / Marc Hallin / Miroslav Siman
12.2.1.4.Relation to halfspace depth / Marc Hallin / Miroslav Siman
12.2.2.Directional Koenker-Bassett methods / Marc Hallin / Miroslav Siman
12.2.2.1.Location case (p = 0) / Marc Hallin / Miroslav Siman
12.2.2.2.(Nonparametric) regression case (p > or = to 1) / Marc Hallin / Miroslav Siman
12.3.Direct approaches / Marc Hallin / Miroslav Siman
12.3.1.Spatial (geometric) quantile methods / Miroslav Siman / Marc Hallin
12.3.1.1.A spatial check function / Miroslav Siman / Marc Hallin
12.3.1.2.Linear spatial quantile regression / Marc Hallin / Miroslav Siman
12.3.1.3.Nonparametric spatial quantile regression / Marc Hallin / Miroslav Siman
12.3.2.Elliptical quantiles / Marc Hallin / Miroslav Siman
Note continued: 12.3.2.1.Location case / Marc Hallin / Miroslav Siman
12.3.2.2.Linear regression case / Miroslav Siman / Marc Hallin
12.3.3.Depth-based quantiles / Marc Hallin / Miroslav Siman
12.3.3.1.Halfspace depth quantiles / Marc Hallin / Miroslav Siman
12.3.3.2.Monge-Kantorovich quantiles / Miroslav Siman / Marc Hallin
12.4.Some other concepts, and applications / Miroslav Siman / Marc Hallin
12.5.Conclusion / Marc Hallin / Miroslav Siman
13.1.Introduction / Manuel Arellano / Stephane Bonhomme
13.2.Heckman's parametric selection model / Stephane Bonhomme / Manuel Arellano
13.2.1.Two-step estimation in Gaussian models / Manuel Arellano / Stephane Bonhomme
13.3.A quantile generalization / Manuel Arellano / Stephane Bonhomme
13.3.1.A quantile selection model / Stephane Bonhomme / Manuel Arellano
13.3.2.Estimation / Manuel Arellano / Stephane Bonhomme
13.4.Identification / Manuel Arellano / Stephane Bonhomme
Note continued: 13.5.Other approaches / Manuel Arellano / Stephane Bonhomme
13.5.1.A likelihood approach / Manuel Arellano / Stephane Bonhomme
13.5.2.Control function approaches / Stephane Bonhomme / Manuel Arellano
13.5.3.Link to censoring corrections / Manuel Arellano / Stephane Bonhomme
13.6.Empirical illustration / Manuel Arellano / Stephane Bonhomme
13.7.Conclusion / Stephane Bonhomme / Manuel Arellano
14.1.Introduction / Joydeep Chowdhury / Probal Chaudhuri
14.2.Regression quantiles in Banach spaces / Joydeep Chowdhury / Probal Chaudhuri
14.3.Nonparametric estimation / Probal Chaudhuri / Joydeep Chowdhury
14.4.Data analysis / Probal Chaudhuri / Joydeep Chowdhury
14.4.1.Simulation / Joydeep Chowdhury / Probal Chaudhuri
14.4.2.Tecator data / Joydeep Chowdhury / Probal Chaudhuri
14.4.3.Pediatric airway data / Probal Chaudhuri / Joydeep Chowdhury
14.4.4.Cigarette data / Joydeep Chowdhury / Probal Chaudhuri
Note continued: 14.4.4.1.Regression of price curve on sales curve / Joydeep Chowdhury / Probal Chaudhuri
14.5.Consistency / Joydeep Chowdhury / Probal Chaudhuri
14.5.1.Additional mathematical details / Probal Chaudhuri / Joydeep Chowdhury
14.6.Concluding remarks / Probal Chaudhuri / Joydeep Chowdhury
15.1.Introduction / Alexandre Belloni / Victor Chernozhukov / Kengo Kato
15.2.Estimation of the conditional quantile function / Alexandre Belloni / Victor Chernozhukov / Kengo Kato
15.2.1.Regularity conditions / Alexandre Belloni / Victor Chernozhukov / Kengo Kato
15.2.2.Li-penalized quantile regression / Alexandre Belloni / Victor Chernozhukov / Kengo Kato
15.2.3.Refitted quantile regression after selection / Alexandre Belloni / Kengo Kato / Victor Chernozhukov
15.2.4.Group lasso for quantile regression models / Alexandre Belloni / Victor Chernozhukov / Kengo Kato
Note continued: 15.2.5.Estimation of the conditional density / Alexandre Belloni / Victor Chernozhukov / Kengo Kato
15.3.Confidence bands for the coefficient process / Alexandre Belloni / Victor Chernozhukov / Kengo Kato
15.3.1.Construction of an orthogonal score function / Alexandre Belloni / Victor Chernozhukov / Kengo Kato
15.3.2.Regularity conditions / Alexandre Belloni / Victor Chernozhukov / Kengo Kato
15.3.3.Score function estimator / Alexandre Belloni / Kengo Kato / Victor Chernozhukov
15.3.4.Double selection estimator / Alexandre Belloni / Kengo Kato / Victor Chernozhukov
15.3.5.Confidence bands / Alexandre Belloni / Kengo Kato / Victor Chernozhukov
15.3.6.Confidence bands via inverse statistics / Alexandre Belloni / Kengo Kato / Victor Chernozhukov
16.1.Introduction / Lan Wang
16.2.High-dimensional sparse linear quantile regression / Lan Wang
Note continued: 16.2.1.Background on penalized high-dimensional regression and the choice of penalty function / Lan Wang
16.2.2.Nonconvex penalized high-dimensional linear quantile regression / Lan Wang
16.2.2.1.Overview / Lan Wang
16.2.2.2.Oracle property of the nonconvex penalized quantile regression estimator / Lan Wang
16.3.High-dimensional sparse semiparametric quantile regression / Lan Wang
16.3.1.Overview / Lan Wang
16.3.2.Nonconvex penalized partially linear additive quantile regression / Lan Wang
16.3.3.Oracle properties / Lan Wang
16.4.Computational aspects of nonconvex penalized quantile regression / Lan Wang
16.4.1.Linear programming based algorithms (moderately large p) / Lan Wang
16.4.2.New iterative coordinate descent algorithm (larger p) / Lan Wang
16.5.Other related problems / Lan Wang
16.5.1.Simultaneous estimation and variable selection at multiple quintiles / Lan Wang
Note continued: 16.5.2.Two-stage analysis with quantile-adaptive screening / Lan Wang
16.5.2.1.Background / Lan Wang
16.5.2.2.Quantile-adaptive model-free nonlinear screening / Lan Wang
16.6.Discussion / Lan Wang
17.1.Introduction / Zhijie Xiao
17.2.Quantile regression estimation of traditional time series models / Zhijie Xiao
17.2.1.Quantile regression estimation of the traditional AR model / Zhijie Xiao
17.2.2.Quantile regressions of other time series models with i.i.d. errors / Zhijie Xiao
17.2.3.Quantile regression estimation of ARMA models / Zhijie Xiao
17.2.4.Quantile regressions with serially correlated errors / Zhijie Xiao
17.3.Quantile regressions with ARCH/GARCH errors / Zhijie Xiao
17.4.Quantile regressions with heavy-tailed errors / Zhijie Xiao
17.5.Quantile regression for nonstationary time series / Zhijie Xiao
17.5.1.Quantile regression for trending time series / Zhijie Xiao
Note continued: 17.5.2.Unit-root quantile regressions / Zhijie Xiao
17.5.3.Quantile regression on cointegrated time series / Zhijie Xiao
17.6.The QAR process / Zhijie Xiao
17.6.1.The linear QAR process / Zhijie Xiao
17.6.2.Nonlinear QAR models / Zhijie Xiao
17.6.3.Quantile autoregression based on transformations / Zhijie Xiao
17.7.Other dynamic quantile models / Zhijie Xiao
17.8.Quantile spectral analysis / Zhijie Xiao
17.8.1.Quantile cross-covariances and quantile spectrum / Zhijie Xiao
17.8.2.Quantile periodograms / Zhijie Xiao
17.8.3.Relationship to quantile regression on harmonic regressors / Zhijie Xiao
17.8.4.Estimation of quantile spectral density / Zhijie Xiao
17.9.Quantile regression based forecasting / Zhijie Xiao
17.10.Conclusion / Zhijie Xiao
18.1.Introduction / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.2.Extreme quantile models / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
Note continued: 18.2.1.Pareto-type and regularly varying tails / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.2.2.Extremal quantile regression models / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.Estimation and inference methods / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.1.Sampling conditions / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.2.Univariave case: Marginal quantiles / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.2.1.Extreme order approximation / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.2.2.Intermediate order approximation / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.2.3.Estimation of / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.2.4.Estimation of AT / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
Note continued: 18.3.2.5.Computing quantiles of the limit extreme value distributions / Victor Chernozhukov / Ivan Fernandez-Val / Tetsuya Kaji
18.3.2.6.Median bias correction and confidence intervals / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.2.7.Extrapolation estimator for very extremes / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.3.Multivariate case: Conditional quantiles / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.3.1.Extreme order approximation / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.3.2.Intermediate order approximation / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.3.3.Estimation of and 7 / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.3.4.Estimation of AT / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
Note continued: 18.3.3.5.Computing quantiles of the limit extreme value distributions / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.3.6.Median bias correction and confidence intervals / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.3.7.Extrapolation estimator for very extremes / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.3.4.Extreme value versus normal inference / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.4.Empirical applications / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.4.1.Value-at-risk prediction / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
18.4.2.Contagion of financial risk / Victor Chernozhukov / Tetsuya Kaji / Ivan Fernandez-Val
19.1.Introduction / Kengo Kato / Antonio F. Galvao
19.2.Panel quantile regression model / Kengo Kato / Antonio F. Galvao
19.3.Fixed effects estimation / Kengo Kato / Antonio F. Galvao
Note continued: 19.3.1.FE-QR estimator / Kengo Kato / Antonio F. Galvao
19.3.2.FE-SQR estimator / Kengo Kato / Antonio F. Galvao
19.3.2.1.Bias correction: Analytical method / Kengo Kato / Antonio F. Galvao
19.3.2.2.Bias correction: Jackknife / Kengo Kato / Antonio F. Galvao
19.3.3.Alternative FE approaches / Kengo Kato / Antonio F. Galvao
19.3.3.1.Shrinkage / Kengo Kato / Antonio F. Galvao
19.3.3.2.Minimum distance / Kengo Kato / Antonio F. Galvao
19.3.3.3.Two-step estimation of Canay (2011) / Kengo Kato / Antonio F. Galvao
19.4.Correlated random effects / Kengo Kato / Antonio F. Galvao
19.5.Extensions / Kengo Kato / Antonio F. Galvao
19.5.1.Endogeneity / Kengo Kato / Antonio F. Galvao
19.5.2.Censoring / Kengo Kato / Antonio F. Galvao
19.5.3.Group-level treatments / Kengo Kato / Antonio F. Galvao
19.5.4.Semiparametric QR for longitudinal data / Kengo Kato / Antonio F. Galvao
19.6.Conclusion / Kengo Kato / Antonio F. Galvao
Note continued: 20.1.Introduction / Zhijie Xiao / Oliver Linton
20.2.Quantile regression in risk management / Zhijie Xiao / Oliver Linton
20.2.1.Value-at-risk / Zhijie Xiao / Oliver Linton
20.2.2.Expected shortfall / Oliver Linton / Zhijie Xiao
20.3.Upper quantile information and financial markets / Zhijie Xiao / Oliver Linton
20.4.Quantile regression and portfolio allocation / Zhijie Xiao / Oliver Linton
20.4.1.The mean-ES portfolio construction / Oliver Linton / Zhijie Xiao
20.4.2.The multi-quantile portfolio construction / Zhijie Xiao / Oliver Linton
20.5.Stochastic dominance and quantile regression / Oliver Linton / Zhijie Xiao
20.6.Quantile dependence / Zhijie Xiao / Oliver Linton
20.6.1.Directional predictability via the quantilogram / Zhijie Xiao / Oliver Linton
20.6.2.Causality in quantiles / Zhijie Xiao / Oliver Linton
20.7.Concluding remarks / Zhijie Xiao / Oliver Linton
Note continued: 21.1.Introduction / Laurent Briollais / Gilles Durrieu
21.2.Genetic applications / Laurent Briollais / Gilles Durrieu
21.2.1.Background and definitions / Laurent Briollais / Gilles Durrieu
21.2.2.Candidate gene association study of child BMI / Gilles Durrieu / Laurent Briollais
21.2.3.GWAS of birthweight / Gilles Durrieu / Laurent Briollais
21.2.4.Genetic association with a set of markers / Gilles Durrieu / Laurent Briollais
21.3.Genomic and other -omic applications / Gilles Durrieu / Laurent Briollais
21.3.1.Background / Laurent Briollais / Gilles Durrieu
21.3.2.Genomic data pre-processing / Laurent Briollais / Gilles Durrieu
21.3.3.Sample size determination in gene expression studies / Laurent Briollais / Gilles Durrieu
21.3.4.Determination of chromosomal region aberrations / Laurent Briollais / Gilles Durrieu
21.3.5.Robust estimation and outlier determination in genomics / Gilles Durrieu / Laurent Briollais
Note continued: 21.3.6.Genomic analysis of set of genes / Laurent Briollais / Gilles Durrieu
21.4.Conclusion / Gilles Durrieu / Laurent Briollais
22.1.Introduction / Brian S. Cade
22.2.Water quality trends over time / Brian S. Cade
22.2.1.A single site within a watershed / Brian S. Cade
22.2.2.Multiple sites within a watershed / Brian S. Cade
22.2.3.Estimation with below-detection limit values in a single site within a watershed / Brian S. Cade
22.2.4.Additional extensions possible for water quality and flow trend analyses / Brian S. Cade
22.3.Herbaceous plant species diversity and atmospheric nitrogen deposition / Brian S. Cade
22.3.1.Quantile regression estimates / Brian S. Cade
22.3.2.Partial effects of nitrogen deposition and pH and critical loads / Brian S. Cade
22.3.3.Additional possible refinements to the model / Brian S. Cade
22.4.Discussion / Brian S. Cade.