My poor little geologist brain hurts...
Perry Collier
Qld, Australia
-----Original Message-----
From: Gerald van den Boogaart [mailto:[EMAIL PROTECTED]]
Sent: Monday, 10 October 2005 6:19 PM
To: Edward Isaaks
Cc: AI-GEOSTATS
Subject: Re: [ai-geostats] How to calculate an unbiased estimate of
variance from a set of weighted samples
Just a comment on Edward Isaaks summary:
> is the "best" one. By "best, I mean the estimator which minimizes bias, or
> better yet, is unbiased.
The standard meaning of "best" in statistics and geostatistics is not
"minimizing bias", but "minizing expected squared error (=Variance+squared
bias)" and is typically used in the construction: "best unbiased", which is
an abbreviation of "the best under all unbiased"
More precisily the "best unbiased" estimator is taken from the set of all
"unbiased" estimators and has minimal variance among them. Thus it is always
unbiased.
Estimation theory says: There are (infinitly) many "not best" but unbiased
estimators (the affine Hilbertspace spanned by the best plus the so called
0-estimators) and often there are (also infinitly many) biased estimators
(e.g. Stein-estimators) uniformly better than the "best unbiased" estimator.
The pure Term "best" estimator is defined as "the estimator with minimal
expected squared error uniformly for all possible true values". However this
globally best estimator only exists in very strange situations.
Best regards,
Gerald v.d. Boogaart
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