Quantile Regression

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Quantile RegressionRoger Koenker and Kevin F. HallockWe say that a student scores at thetth Quantile of a standardized exam ifhe performs better than the proportiontof the reference group ofstudents and worse than the proportion (1 t). Thus, half of studentsperform better than the median student and half perform worse. Similarly, thequartiles divide the population into four segments with equal proportions of thereference population in each segment. The quintiles divide the population into fiveparts; the deciles into ten parts.

To illustrate the basic ideas, we briefly reconsider a classical empirical appli-cation in economics, Engel’s (1857) analysis of the relationship between household food expenditure and household income. In Figure 3, we plot Engel’s data taken from 235 European working-class households. Superimposed on the plot are seven

  Action, Regression, Appli cation, Appli, Quantile, Quantile regression