Stata The Stata listserver
[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

Re: st: qreg SEs


From   Ricardo Ovaldia <ovaldia@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: qreg SEs
Date   Thu, 27 Feb 2003 12:53:50 -0800 (PST)

Bobby and Scott, 

Thank you for the information. 

Ricardo.

--- "Roberto G. Gutierrez, StataCorp."
<rgutierrez@stata.com> wrote:
> In the midst of the fray of posts on -qreg- standard
> errors, Scott Merryman
> <smerryman@kc.rr.com> offers:
> 
> [...]
> > "Their results [Koenker and Bassett (1978,1982),
> Huber (1967) Rogers(1993)
> > and Stata (1997)] suggest an estimator for the
> asymptotic covariance matrix
> > of the quantile regression estimator,
> 
> >             Est. Asy. Var[b] =
> (X'X)^-1(X'DX)(X'X)^-1
> 
> > Where D is a diagonal matrix containing weights
> 
> >  d = [q/f(0)]^2 if y - xB > 0 and [(1-q)/f(0)]^2
> otherwise
> 
> > and f(0) is the true density of the disturbances
> evaluated at 0.  There is,
> > at this point, a rather large hole in the theory.
> How one is to know f(0) is
> > unclear.  Moreover, if one knew the true density,
> then the maximum
> > likelihood estimator would be a preferable, and
> available, estimator.
> > ......The bootstrap method of inferring
> statistical properties is well
> > suited for this application.  Since the efficacy
> of the bootstrap has been
> > established for this purpose, the search for a
> formula for standard errors
> > of the LAD estimator is not really necessary."
> 
> > Koenker has a couple papers on quantile regression
> you may want to take a
> > look at:
>
http://www.econ.uiuc.edu/~roger/research/intro/intro.html
> (also, I
> > believe, volume 26 of Empirical Economics was
> devoted to applications of
> > quantile regression).
> 
> > In Koenker and Hallock's paper "Quantile
> Regression: An Introduction" (the
> > longer version) they write (page 16):
> 
> > "Stata's command qreg also produces estimates of
> asymptotic standard errors
> > based on iid error assumptions. Although they are
> designated as
> > "Koenker-Bassett standard errors" the method bears
> little resemblance to the
> > histospline approach of the cited reference. As
> described by Rogers (1993)
> > the qreg's standard errors appear to be a variant
> of the iid Siddiqui method
> > with a rather unfortunate choice of bandwidth.[see
> footnote 6] A consequence
> > of the undersmoothing implied by the Stata rule is
> that the resulting
> > standard errors are frequently considerably
> smaller than would be obtained
> > with a more conventional bandwidth selection rule.
> This conclusion is
> > supported by the Monte Carlo comparison reported
> in Rogers (1992)."
> 
> > This is discussed briefly in the reference manual
> [R] qreg (page 276).
> > Koenker uses the Hall and Sheather (1988)
> bandwidth rule in his S and R
> > implementation.
> 
> Scott pretty much gives the whole story here, and as
> a result has made my post
> much shorter than what was originally planned.  I'll
> simply add that it has
> been our plan for some time to improve on our ad hoc
> estimate of f(0), as
> implemented in -qreg-.  This remains on our list of
> things to do.
> 
> --Bobby
> rgutierrez@stata.com
> *
> *   For searches and help try:
> *  
> http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/


__________________________________________________
Do you Yahoo!?
Yahoo! Tax Center - forms, calculators, tips, more
http://taxes.yahoo.com/
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/



© Copyright 1996–2014 StataCorp LP   |   Terms of use   |   Privacy   |   Contact us   |   What's new   |   Site index