Dear all,
I need to run a quantile regression but considering a different objective
function to be minimized: instead of finding the parameters that minimize
rho(t) = u*(t - I(u<0)), I need to find the parameters beta that minimize a sum
of two rho functions rho(t1) = u1*(t1 - I(u1<0)) and rho(t2) = u2*(t2 -
I(u2<0)) where t1 and t2 are different quantile levels and u1 = y1 - b'x1 and
u2 = y2 - b'x2.
y1 and x1 are response variable and regressors, respectively, that will be
weighted by t1 and similar for t2.
The problem is that I do not know how to change the function rq() in R because
it only accepts two arguments, y and x. In my case, I think I also have two
arguments, that is x <- rbind(x1,x2) and y <- rbind(y1,y2) , but I need to
split the residuals to be minimized, weighting u1 by t1 and u2 by t2. I am
trying my best, but I cannot do it.
Does anybody have any suggestion?
I appreciate any kind of suggestion and help.
All the best,
Nathalie
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