[RsR] The robust regression confidence interval‏

[Rand Wilcox]

There are a collection of methods summarized in 

Wilcox, R. R. (2012). Introduction to Robust Estimation and                
Hypothesis Testing 3rd Edition. New York: Elsevier.

Heteroscedasticity is addressed as well. Descriptions and illustrations of R functions are included.



Rand Wilcox
Professor
Dept of Psychology
3620 McClintock Ave
USC
Los Angeles, CA 90089-1061

FAX: 213-746-9082
For information about statistics books and software, see http://college.usc.edu/labs/rwilcox/home

----- Original Message -----
From: Roger Koenker <rkoenker using illinois.edu>
Date: Wednesday, May 8, 2013 9:22 am
Subject: Re: [RsR] The robust regression confidence interval‏
To: Anton Kochepasov <akss using outlook.com>
Cc: "r-sig-robust using r-project.org" <r-sig-robust using r-project.org>

> For quantile regression you can again just use summary(rq(...)).
> 
> 
> url:    www.econ.uiuc.edu/~roger            Roger Koenker
> email    rkoenker using 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                                               
> > _______________________________________________
> > R-SIG-Robust using r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-robust
> 
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