On Tue, 30 May 2000 19:03:49 +0200, Markus Quandt
<[EMAIL PROTECTED]> wrote:
> Hello all,
>
> when discussing linear regression assumptions with a colleague, we
> noticed that we were unable to explain WHY heteroscedasticity has
> the well known ill effects on the estimators' properties. I know
> WHAT the consequences are (loss of efficiency, tendency to
> underestimate the standard errors) and I also know why these
> consequences are undesirable. What I'm lacking is a substantial
> understanding of HOW the presence of inhomogeneous error variances
> increases the variability of the coefficients, and HOW the
> estimation of the standard errors fails to reflect this.
I think I learned this from an article by N. Cressie, about t-tests.
Think of, the Variance of the variance ...
- one way to think of it: Heterogeneity makes your system with
100 or 1000 degrees of freedom act as if it had just a tiny DF.
This shows up in the "variance of the variance" -- you pool
two groups with unequal N for a t-test, or don't pool them. The
Satterthwaite correction to DF gives one estimate of how the
difference behaves.
(If the tiny group has a big variance, and small DF, the Difference
has a big variance and *effectively* small DF; because of the
variance of the variance.)
Similarly, if you draw a plot of two variables and they both have two
or three outliers at one end, the *effective* DF of the relation
depends on how many outliers there are. Check on how the
"significance" of the correlation depends on the DF.
This is not precise, but I maybe it helps ...
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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