Quantile regression. Volume 2, Estimation and simulation

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Title:

Author:

Furno, Marilena, 1957- author.

ISBN:

9781118863602

9781118863640

9781118863671

9781118863718

Physical Description:

1 online resource

General Note:

6.3.1 Related tests for unit root.

Contents:

Cover; Title Page; Copyright; Contents; Preface; Acknowledgements; Introduction; About the companion website; Chapter 1 Robust regression; Introduction; 1.1 The Anscombe data and OLS; 1.2 The Ancombe data and quantile regression; 1.2.1 Real data examples: the French data; 1.2.2 The Netherlands example; 1.3 The influence function and the diagnostic tools; 1.3.1 Diagnostic in the French and the Dutch data; 1.3.2 Example with error contamination; 1.4 A summary of key points; References; Appendix: computer codes in Stata; Chapter 2 Quantile regression and related methods; Introduction.

2.1 Expectiles2.1.1 Expectiles and contaminated errors; 2.1.2 French data: influential outlier in the dependent variable; 2.1.3 The Netherlands example: outlier in the explanatory variable; 2.2 M-estimators; 2.2.1 M-estimators with error contamination; 2.2.2 The French data; 2.2.3 The Netherlands example; 2.3 M-quantiles; 2.3.1 M-quantiles estimates in the error-contaminated model; 2.3.2 M-quantiles in the French and Dutch examples; 2.3.3 Further applications: small-area estimation; 2.4 A summary of key points; References; Appendix: computer codes.

Chapter 3 Resampling, subsampling, and quantile regressionIntroduction; 3.1 Elemental sets; 3.2 Bootstrap and elemental sets; 3.3 Bootstrap for extremal quantiles; 3.3.1 The French data set; 3.3.2 The Dutch data set; 3.4 Asymptotics for central-order quantiles; 3.5 Treatment effect and decomposition; 3.5.1 Quantile treatment effect and decomposition; 3.6 A summary of key points; References; Appendix: computer codes; Chapter 4 A not so short introduction to linear programming; Introduction; 4.1 The linear programming problem; 4.1.1 The standard form of a linear programming problem.

4.1.2 Assumptions of a linear programming problem4.1.3 The geometry of linear programming; 4.2 The simplex algorithm; 4.2.1 Basic solutions; 4.2.2 Optimality test; 4.2.3 Change of the basis: entering variable and leaving variable; 4.2.4 The canonical form of a linear programming problem; 4.2.5 The simplex algorithm; 4.2.6 The tableau version of the simplex algorithm; 4.3 The two-phase method; 4.4 Convergence and degeneration of the simplex algorithm; 4.5 The revised simplex algorithm; 4.6 A summary of key points; References; Chapter 5 Linear programming for quantile regression; Introduction.

5.1 LP formulation of the L1 simple regression problem5.1.1 A first formulation of the L1 regression problem; 5.1.2 A more convenient formulation of the L1 regression problem; 5.1.3 The Barrodale-Roberts algorithm for L1 regression; 5.2 LP formulation of the quantile regression problem; 5.3 Geometric interpretation of the median and quantile regression problem: the dual plot; 5.4 A summary of key points; References; Chapter 6 Correlation; Introduction; 6.1 Autoregressive models; 6.2 Non-stationarity; 6.2.1 Examples of non-stationary series; 6.3 Inference in the unit root model.

Abstract:

Contains an overview of several technical topics of Quantile Regression Volume two of Quantile Regression offers an important guide for applied researchers that draws on the same example-based approach adopted for the first volume. The text explores topics including robustness, expectiles, m-quantile, decomposition, time series, elemental sets and linear programming. Graphical representations are widely used to visually introduce several issues, and to illustrate each method. All the topics are treated theoretically and using real data examples. Designed as a practical resource, the book is thorough without getting too technical about the statistical background. The authors cover a wide range of QR models useful in several fields. The software commands in R and Stata are available in the appendixes and featured on the accompanying website. The text: Provides an overview of several technical topics such as robustness of quantile regressions, bootstrap and elemental sets, treatment effect estimators Compares quantile regression with alternative estimators like expectiles, M-estimators and M-quantiles Offers a general introduction to linear programming focusing on the simplex method as solving method for the quantile regression problem Considers time-series issues like non-stationarity, spurious regressions, cointegration, conditional heteroskedasticity via quantile regression Offers an analysis that is both theoretically and practical Presents real data examples and graphical representations to explain the technical issues Written for researchers and students in the fields of statistics, economics, econometrics, social and environmental science, this text offers guide to the theory and application of quantile regression models.

Local Note:

John Wiley and Sons

Subject Term:

Quantile regression.

Regression analysis.

Régression quantile.

Analyse de régression.

Probability & Statistics.

MATHEMATICS.

Regression analysis

Quantile regression

Genre: