Bobby and Scott,
Thank you for the information.
Ricardo.
--- "Roberto G. Gutierrez, StataCorp."
<[email protected]> wrote:
> In the midst of the fray of posts on -qreg- standard
> errors, Scott Merryman
> <[email protected]> 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
> [email protected]
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