Hello Everyone,
I'm currently learning about quantile regressions. I've been using an
optimizer to compare with the rq() command for quantile regression.
When I run the code, the results show that my coefficients are consistent
with rq(), but the intercept term can vary by a lot.
I don't think my optimizer code is wrong and suspects it has something to do
with the starting values.
The results seems very sensitive to different starting values and I don't
know how to make sense of it.
Advice from the community would be greatly appreciated.
Sincerely,
Kevin Chang
###################### CODE Below ###########################
library(quantreg)
data(engel)
y<-cbind(engel[,2])
x<-cbind(rep(1,length(engel[,1])),engel[,1])
x1<-cbind(engel[,1])
nn<-nrow(engel)
nn
bhat.ls<-solve(t(x)%*%x)%*%t(x)%*%y
#bhat.ls
# QUANTILES
quant=.25
fr.1=function(bhat.opt)
{
uu=y-x%*%bhat.opt
sample.cond.quantile=quantile(uu,quant)
w.less=rep(0,nn)
for(ii in 1:nn){if(uu[ii]<sample.cond.quantile) w.less[ii]=1}
sum((quant-1)*sum((y-x%*%bhat.opt)*w.less) #negative residuals
+quant*sum((y-x%*%bhat.opt)*(1-w.less))) #positive residuals
}
start<-c(0,0)
result=optim(start,fr.1)
bhat.cond=result$par
#Quantile Command Results
fit.temp=rq(y~x1,tau=quant)
fit.temp
#OPTIMIZER Results
bhat.cond
#OLS Command Results
mean=lm(y~x1)
mean
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