Mathematics
The mathematical forms arising from quantile regression are distinct from those arising in the method of least squares. The method of least squares leads to a consideration of problems in an inner product space, involving projection onto subspaces, and thus the problem of minimizing the squared errors can be reduced to a problem in numerical linear algebra. Quantile regression does not have this structure, and instead leads to problems in linear programming that can be solved by the simplex method. The fact that the algorithms of linear programming appear more esoteric to some users may explain partially why quantile regression has not been as widely used as the method of least squares.
Read more about this topic: Quantile Regression
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