Re: Gaussian variance estimation

David Delgado Gomez <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> Good morning,
> 
> I have data with a normal distribution.  Values higher than the mean are
> corrupted with noise. Is it possible to estimate the variance of the
> gaussian distribution just taking into account values smaller than the
> mean?
> Thanks
> David

Some others have already commented, but I'll add my $0.02.

As often is the case, we might be able to give more useful answers
if we had more information.  If we take what you've written at face
value, then you would appear to know a lot about the process that
generated the data that could be applied to the problem, i.e. you
know (somehow) that the distribution is normal (Herman Rubin might
say it isn't normal ;-) ), and you know (somehow) that only the
values higher than the mean are corrupted (implying you know the
mean, too).  Perhaps you also know (somehow) the characteristics
of the noise?

Someone's suggestion that you simply reflect the data less than the
mean to above the mean and calculate the sample variance seems like
an easy, practical solution as a first cut, with the caveat that
the result would have, I think, a higher uncertainty than one would
get from the same number of "real" values.  Depending on how much
work it is worth to get a result, here's another idea.  If you know
mean and the characteristics of the noise, you can generate many
samples of normal values plus noise with specified variances, and
compare those to the observed distribution (with something like a
K-S test, for instance).  Pick the variance that generates
distributions closest to the observations.  You probably want to
generate a number of samples of "fake" data for each proposed variance
you want to test, plus maybe using some different values of the
parameters of the noise, too.  You should be able to start with
something fairly close to the "true" variance by taking the variance
from the corrupted sample (if it doesn't spread the observed
distribution too much) or getting a starting value with the
"reflection" method given above.  It's a bit of work, and only
doable if you have enough information, but it might be worth it
if you really need to convince somebody about the results (like
your dissertation commitee).

Regards,
Russell