I am working on Quantile Regression (QR) and want to assess models using goodness of fit (GOF) measures. I have come across the post here, here that says, AIC/BIC can be calculated for QR model besides R squared as GOF. My questions are;
- Does estimation of QR coefficient involve Maximization of a Likelihood function? If not, how is AIC calculated there? (As per my knowledge, coefficients are estimated using Linear Programming algorithms. I know nothing about the algorithm used there though.)
- Can two competing models be tested using AIC values, same as in case of other methods?