[RsR] The robust regression confidence interval‏

For quantile regression you can again just use summary(rq(...)).


url:    www.econ.uiuc.edu/~roger            Roger Koenker
email    rkoenker at uiuc.edu            Department of Economics
vox:     217-333-4558                University of Illinois
fax:       217-244-6678                Urbana, IL 61801

On May 8, 2013, at 10:51 AM, Anton Kochepasov wrote:

Hi everyone,

A few years ago there was a discussion about a robust regression 

confidence interval (https://stat.ethz.ch/pipermail/r-sig-
robust/2008/000217.html) and I would like to resort your courtesy 
again.> 

I'm trying to compare a few regression models for my data. For 

linear regression everything is quite understandable, but robust 
and quantile regressions are not so obvious. I could not find 
almost anything about calculating confidence interval for these 
regression models unless I looked for something wrong.

My code in R looks as follows:
# Robust linear modeling
library(MASS)
library(robustbase)
library(robust)
set.seed(343); 
x <- rnorm(1000)
y <- x + 2*rnorm(1000)

lm1<-lm(y~x); rlm1<-rlm(y~x); rlm2 <- lmRob(y~x); rlm3 <- lmrob(y~x)
cbind(summary(lm1)$coeff,  confint(lm1)) 
cbind(summary(rlm1)$coeff, confint(rlm1))
cbind(summary(rlm2)$coeff, confint(rlm2))
cbind(summary(rlm3)$coeff, confint(rlm3))

And produces the following result:

cbind(summary(lm1)$coeff,  confint(lm1))

               Estimate Std. Error   t value     Pr(>|t|)      

2.5 %     97.5 %

(Intercept) -0.06973191 0.06408983 -1.088034 2.768429e-01 -

0.1954982 0.05603438

x            0.97647196 0.06619635 14.751145 1.071805e-44  

0.8465720 1.10637196

cbind(summary(rlm1)$coeff, confint(rlm1))

                  Value Std. Error    t value 2.5 % 97.5 %
(Intercept) -0.06131788 0.06714405 -0.9132288    NA     NA
x            0.96016596 0.06935096 13.8450275    NA     NA

cbind(summary(rlm2)$coeff, confint(rlm2))

Error in UseMethod("vcov") : 
  no applicable method for 'vcov' applied to an object of class 

"lmRob">> cbind(summary(rlm3)$coeff, confint(rlm3))

              Estimate Std. Error    t value     Pr(>|t|)      

2.5 %     97.5 %

(Intercept) -0.0568964 0.06608987 -0.8608945 3.895029e-01 -

0.1865874 0.07279464

x            0.9612520 0.06821558 14.0913850 2.921913e-41  

0.8273896 1.09511448

It's easy to spot that linear model works OK and only one robust 

regression gives a sensible result. Another observation is that 
lmrob(), which produces some actual confidence interval, calculates 
it in the same manner as lm(), with using 1.96 as the student 
coefficient.> 

Could you share your opinion if it is a correct way to produce a 

confidence interval for the robust regression model (same as for 
the linear regression)? May the same method be used for the 
quantile regression model? If not, what should I use?

Thank you in advance,
Anton