Quantile regression is uniquely powerful for identifying "limiting constraints" on populations. For example, in public health, it can reveal if a treatment benefits those at the highest risk (the upper quantiles) differently than those at lower risk, providing a complete "statistical landscape" rather than just a single point of view. Practical Implementation
: It moves beyond standard quantiles to compare them with expectiles, M-estimators, and M-quantiles , offering a more robust toolkit for dealing with outliers and non-normal distributions. Quantile Regression Volume 2 Estimation and Sim...
: At its core, estimating quantiles is an optimization problem. The book provides a "softened" mathematical journey into linear programming, using the simplex algorithm and two-phase methods to solve the quantile regression framework. : At its core, estimating quantiles is an
Understanding the Full Distribution: A Deep Dive into Quantile Regression (Volume 2) : At its core