Quantile Regression: Theory and Applications.pdf
Preface Acknowledgements Introduction 1 A Visual Introduction to Quantile Regression 1.1 The Essential Toolkit 1.1.1 Unconditional Mean, Unconditional Quantiles and Surroundings 1.1.2 Technical Insight: Quantiles as Solutions of a Minimization Problem 1.1.3 Conditional Mean, Conditional Quantiles and Surroundings 1.2 The Simplest QR Model: the Case of the Dummy Regressor 1.3 A Slightly More Complex QR Model: the Case of a Nominal Regressor 1.4 A Typical QR Model: the Case of a Quantitative Regressor 1.5 A Summary of Key Points References 2 Quantile Regression: Understanding How and Why 2.1 How and Why Quantile Regression Works 2.1.1 The General Linear Programming Problem 2.1.2 The Linear Programming Formulation for the QR Problem 2.1.3 Methods for Solving the Linear Programming Problem 2.2 A Set of Illustrative Artificial Data 2.2.1 Homogeneous Error Models 2.2.2 Heterogeneous Error Models 2.2.3 Dependent Data Error Models 2.3 How and Why to Work with Quantile Regression 2.3.1 QR for Homogeneous and Heterogeneous Models 2.3.2 QR Prediction Intervals 2.3.3 A Note on the Quantile Process 2.4 A Summary of Key Points References 3 Estimated Coefficients and Inference 3.1 Empirical Distribution of the Quantile Regression Estimator 3.1.1 The Case of Indipendent Identically Distributed Errors 3.1.2 The Case of Non-Identically Distributed Errors 3.1.3 The Case of Dependent Errors 3.2 Inference in Quantile Regression, the i.i.d. Case 3.3 Wald, Lagrange Multipliers, Likelihood Ratio Test 3.4 A Summary of Key Points References 4 Additional Tools for the Interpretation and Evaluation of the Quantile Regression Model 4.1 Data Pre--Processing 4.1.1 Explanatory Variable Transformations 4.1.2 Dependent Variable Transformations 4.2 Response Conditional Density Estimations 4.2.1 The Case of Different Scenario Simulations 4.2.2 The Case of the Response Variable Reconstruction 4.3 Validation of the Model 4.3.1 Goodness of Fit 4.3.2 Resampling Methods 4.4 A Summary of Key Points References 5 Models with Dependent and with Non-Identically Distributed Data 5.1 A Closer Look at the Scale Parameter, the i.i.d Case 5.1.1 Estimating the Variance of Quantile Regressions 5.1.2 Confidence Intervals and Hypothesis Testing on the Estimated Coefficients 5.1.3 Example for the i.i.d. Case 5.2 The Non Identically Distributed Case 5.2.1 Example for the Non Identically Distributed Case 5.2.2 Quick Ways to Test Equality of Coefficients across Quantiles in Stata 5.2.3 The Wage Equation Revisited 5.3 The Dependent Data Model 5.3.1 Example with Dependent Data 5.4 A Summary of Key Points 1 References 6 Additional Models 6.1 Nonparametric Quantile Regression 6.1.1 Local Polynomial Regression 6.1.2 Quantile Smoothing Splines 6.2 Nonlinear Quantile Regression 6.3 Censored Quantile Regression 6.4 Longitudinal data 6.5 Group Effect Quantile Regression 6.6 Binary Quantile Regression 6.7 A Summary of Key Points References A Quantile Regression and Surroundings Using R A.1 Loading Data A.1.1 Text Data A.1.2 Spreadsheet Data A.1.3 Files from Other Statistical Packages A.2 Exploring Data A.2.1 Graphical Tools A.2.2 Summary Statistics A.3 Modelling Data A.3.1 OLS Regression Analysis A.3.2 QR Regression Analysis A.4 Exporting Figures and Tables References B Quantile Regression Analysis and Surroundings Using SAS B.1 Loading Data B.1.1 Text Data B.1.2 Spreadsheet Data B.1.3 Files from Other Statistical Packages B.2 Exploring Data B.2.1 Graphical Tools B.2.2 Summary Statistics B.3 Modelling Data B.3.1 OLS Regression Analysis B.3.2 QR Regression Analysis B.4 Exporting Figures and Tables References C Quantile Regression and Surroundings Using Stata C.1 Loading Data C.1.1 Text Data C.1.2 Spreadsheet Data C.1.3 Files from Other Statistical Packages C.2 Exploring Data C.2.1 Graphical Tools C.2.2 Summary Statistics C.3 Modelling Data C.3.1 OLS Regression Analysis C.3.2 QR Regression Analysis C.4 Exporting Figures and Tables References Index
This unique reference offers a balance between methodology and application, illustrating how and why to use quantile regression in a variety of areas such as economics, finance and computing. It presents a complete treatment of quantile regression methods, including basic modeling, geometrical interpretation, estimation and inference issues, and diagnostic tools. Each method is explained and illustrated with examples using real data, including datasets for exchange rates and financial portfolios. A companion website hosts R, Stata, and SAS software codes. An essential resource for researchers and students in statistics, economics, econometrics, and chemistry.