Quantile Regression : Logic

[Akanksha Aggarwal]

Hi, I am working on a dataset where I am required to run quantile regressions. I want to understand why weighted sum of absolute errors is minimized in quantile regressions and not sum of squared errors like in least squares.

Would be great if someone could suggest a reading to understand quantile regressions.

[Carlo Lazzaro]

Akankska:
an authoritative textbook on this topic can be found at: https://www.cambridge.org/core/books...37390D44A328B1.

[Joao Santos Silva]

Dear Akanksha Aggarwal,

Carlo already pointed you to the ultimate reference, but a gentle introduction can be found here. Note, however, that if quantile regression minimized the sum of squares of the residuals it would be identical to least squares and would have no interest; so, quantile regression minimizes an alternative measure of goodness-of-fit and identifies quantiles rather than the mean.

Best wishes,

Joao

[Akanksha Aggarwal]

Thanks so much, Carlo and Joao.