Quantile Regression

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. The quantiles, or percentiles, or occasionallyfractiles, refer to the general case. Quantile Regression as introduced by Koenkerand Bassett (1978) seeks to extend these ideas to the estimation ofconditionalquantile functions models in which quantiles of the conditional distribution of theresponse variable are expressed as functions of observed Figure 1, we illustrate one approach to this task based on Tukey s boxplot(as in McGill, Tukey and Larsen, 1978).

least squares line passes above all of the very low income observations. We have occasionally encountered the faulty notion that something like quan-tile regression could be achieved by segmenting the response variable into subsets according to its unconditional distribution and then doing least squares fitting on these subsets.

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  Tesla, Square, Ielts, Regression, Least squares, Quan, Quantile, Quantile regression, Quan tile regression

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