Quantile Regression : Estimation and Simulation, Volume 2.
- 1st ed.
- 1 online resource (310 pages)
- Wiley Series in Probability and Statistics Series .
- Wiley Series in Probability and Statistics Series .
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 Expectiles -- 2.1.1 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 regression -- Introduction -- 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 problem -- 4.1.3 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 problem -- 5.1.1 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 -- 6.3.1 Related tests for unit root -- 6.4 Spurious regression -- 6.5 Cointegration -- 6.5.1 Example of cointegrated variables -- 6.5.2 Cointegration tests -- 6.6 Tests of changing coefficients -- 6.6.1 Examples of changing coefficients -- 6.7 Conditionally heteroskedastic models -- 6.7.1 Example of a conditional heteroskedastic model -- 6.8 A summary of key points -- References -- Appendix: Stata computer codes -- Index -- EULA.