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Quantile Regression

Lingxin Hao and Daniel Q. Naiman
Publisher: Sage
Copyright: 2007
ISBN-13: 978-1-4129-2628-7
Pages: 126; paperback
Price: $18.75

Comment from the Stata technical group

Quantile Regression, by Lingxin Hao and Daniel Q. Naiman, provides an excellent introduction to quantile-regression methods. The intuitive explanations and many examples make this book easy to read and understand. An appendix provides Stata commands to replicate the examples using the datasets available at

After showing the advantages that quantile regression has over least squares, the authors discuss the estimation technique, the statistical inference, and how to interpret the results. The example-based approach is exceptionally clear and avoids swamping the reader in technical details.

The final section of the monograph applies the techniques to changes in U.S. income equality between 1991 and 2001. This application illustrates both how to use the methods and how to interpret the results.

Table of contents

Series Editor’s Introduction
1. Introduction
2. Quantiles and Quantile Functions
CDFs, Quantiles, and Quantile Functions
Sampling Distribution of a Sample Quantile
Quantile-Based Measures of Location and Shape
Quantile as a Solution to a Certain Minimization Problem
Properties of Quantiles
Chapter 2 Appendix: A Proof: Median and Quantiles as Solutions to a Minimization Problem
3. Quantile-Regression Model and Estimation
Linear-Regression Modeling and Its Shortcomings
Conditional-Median and Quantile-Regression Models
QR Estimation
Transformation and Equivariance
4. Quantile-Regression Inference
Standard Errors and Confidence Intervals for the LRM
Standard Errors and Confidence Intervals for the QRM
The Bootstrap Method for the QRM
Goodness of Fit of the QRM
5. Interpretation of Quantile-Regression Estimates
Reference and Comparison
Conditional Means Versus Conditional Medians
Interpretation of Other Individual Conditional Quantiles
Tests for Equivalence of Coefficients Across Quantiles
Using the QRM Results to Interpret Shape Shifts
6. Interpretation of Monotone-Transformed QRM
Location Shifts on the Log Scale
From Log Scale Back to Raw Scale
Graphical View of Log-Scale Coefficients
Shape-Shift Measures from Log-Scale Fits
7. Application to Income Inequality in 1991 and 2001
Observed Income Disparity
Descriptive Statistics
Notes on Survey Income Data
Goodness of Fit
Conditional-Mean Versus Conditional-Median Regression
Graphical View of QRM Estimates from Income and Log-Income Equations
Quantile Regressions at Noncentral Positions: Effects in Absolute Terms
Assessing a Covariate’s Effect on Location and Shape Shifts
Appendix: Stata Codes
About the Authors
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