11.4: End-of-Chapter Materials
- Page ID
- 57761
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)R Functions
In this chapter, we were introduced to several R functions that will be useful in quantile regression. These are listed here.
Packages
quantreg
This package contains many functions associated with quantile regression. This chapter just skimmed the surface of what can be done and what should be checked. As this package is not a part of the base R, you will need to install it before loading it.
Statistics
rq(formula)
This is the function that performs quantile regression. The formula is required. By default, the quantile examined is \(\tau = 0.500\), but that can be changed by specifying the value of that \(\tau\), "tau."summary(model)
This is the familiar command that allows us to see the regression table produced by the regression method. Here, it provides the effect estimates (coefficients) and the central 95% confidence interval for that effect.
Exercises
- In the setting of Example 11.1.1, perform ordinary least squares regression to calculate the effect estimate and its 95% confidence interval.
Applied Readings
- Lingxin Hao and Daniel Q. Naiman (2008). Assessing Inequality. Sage Publishing (Quantitative Applications in the Social Sciences; 166).
Theory Readings
- Ian Barrodale and F. D. K. Roberts (1974). "Solution of an overdetermined system of equations." Communications of the ACM. 17(6), 319–320.
doi: 10.1145/355616.361024 - Lingxin Hao and Daniel Q. Naiman (2007). Quantile Regression. Sage Publishing (Quantitative Applications in the Social Sciences; 149).
- Roger W. Koenker (2005). Quantile Regression. Cambridge University Press.
- Roger W. Koenker and Gilbert W. Bassett, Jr. (1978). "Regression quantiles." Econometrica. 46, 33–50.
- Roger W. Koenker and Kevin F. Hallock (2001). "Quantile Regression." The Journal of Economic Perspectives. 15: 143–156.
- Roger W. Koenker and Vasco D'Orey (1987). "Algorithm 229: Computing regression quantiles." Journal of the Royal Statistical Society. Series C (Applied Statistics). 36: 383–393.
- Roger W. Koenker and Vasco D'Orey (1994). "Remark AS R92: A Remark on Algorithm AS 229: Computing Dual Regression Quantiles and Regression Rank Scores." Journal of the Royal Statistical Society. Series C (Applied Statistics). 43: 410–414.
- Yinbo Li and Gonzalo R. Arce (2004). "A Maximum Likelihood Approach to Least Absolute Deviation Regression." EURASIP Journal on Applied Signal Processing. 12: 1762–1769.
- Yang Shu-guang and Liao Jian-wen (1992). "Solution of an Overdetermined System of Linear Equations in \(L_2\), \(L_\infty\), \(L_p\) Norm Using L.S. Techniques." Journal of Computational Mathematics. 10: 29–38.