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Re: st: robust regression with robust errors

From   "Stas Kolenikov" <>
Subject   Re: st: robust regression with robust errors
Date   Mon, 17 Nov 2008 09:33:11 -0600

On 11/17/08, Diemo Urbig <> wrote:
> Dear stata experts:
>  knowing that "rreg" can be used to deal with violations of
>  distributional assumptions and "reg ,r" for dealing with
>  heteroscedasticity, I ask myself whether and to what extent there is a
>  way to deal with both at the same time. Given that "reg", "reg , r", and
>  "rreg" all yield different results regarding a model and distributional
>  assumptions and heteroscedasticity seem to play a role, is there a way
>  to combine rreg with robust errors?

-rreg- is a reasonably complicated routine (with some switching
between objective functions as far as I can recall), and the procedure
for computing standard errors is even less transparent. Technically
since -rreg- is an M-estimator, one should be able to construct the
analogue of -_robust- sandwich var-cov matrix (although you might have
issues with the -rreg-'s objective function not being smooth enough,
and the bread part of the sandwich requires a derivative).
Realistically most robust regression methods work with some sort of
cut-off points beyond which the influence of the residuals is
downweighted, and allowing for heteroskedasticity means that one
should have a way to have a new influence cut-off for any new
observation -- which is a bit too much to ask: you either believe a
large residual is an outlier that needs to be downplayed by the robust
procedure, or that this is a realization of large variance due to
heteroskedasticity. You cannot do both at the same time, those are
kinda contradictory to one another.

You might want to run a small simulation to see how -rreg- standard
errors actually perform.

Stas Kolenikov, also found at
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