Computational Methods for Quantile Regression

Authored by: Roger Koenker

Handbook of Quantile Regression

Print publication date:  October  2017
Online publication date:  October  2017

Print ISBN: 9781498725286
eBook ISBN: 9781315120256
Adobe ISBN:

10.1201/9781315120256-5

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Abstract

The earliest computation of a median regression estimator is usually attributed to the Croatian Jesuit, Rudjer Boscovich. In 1760 Boscovich visited London and, as recounted by Stigler (1984) and Farebrother (1990), posed the computation problem to Thomas Simpson. In Boscovich’s version of the problem the mean residual was constrained to be zero, a requirement that conveniently reduces the problem to finding a (scalar) weighted median. Thus, the bivariate median regression problem of minimizing the sum of absolute residuals, ? ^ = argmin ( b 0 , b 1 ) ∈ R 2 ∑ i = 1 n | y i - b 0 - b 1 x i | , $$ \hat{\beta }= \text{ argmin}_{(b_0 , b_1) \in \mathbb R ^2} \left\{ \sum _{i=1}^n | y_i - b_0 - b_1 x_i | \right\} , $$

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