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Variance
of a central value
One-on-one
correspondence between central values and variances implies
that an infinite set of distance-weighted
averages has an infinite set of variances. In geostatistics,
incredibly, the infinite set of
variances of kriged estimates vanished without a trace.
Most distance-weighted averages in the infinite set converge
on the arithmetic mean while
most variances of distance-weighted averages converge
on the variance of the arithmetic
mean. Obviously, classical statistics is unforgiving
whenever the fundamental requirements are tinkered with.
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The
central limit theorem describes the relationship
between the variance of a set of measured values
with equal weights and the variance of its arithmetic
mean. In Geostatistical Ore Reserve Estimation,
Chapter 2, page 33, David refers to "the famous
central limit theorem". Yet, the above equations
apply to all weighted averages but are nowhere
to be found in the geostatistical literature! |
| Kriging
variances and covariances
of finite subsets of functionally dependent kriged
estimates are the nuts and
bolts of geostatistics but they are an absurd
aberration in classical statistics. Armstrong
and Champigny, in A Study on Kriging Small Blocks,
do caution against oversmoothing because kriging
variances converge on zero, and kriging covariances
on a coefficient of determination of unity.
Just
the same, the authors intimate that kriging is foolproof
as long as fools do not oversmooth and are unconcerned
about undersmoothing. They are alos unconcerened
about the daunting task of selecting the least biased
and most precise subset of the infinite set of kriged
estimates. |
"It
seems very pretty but's rather hard to understand.
Somehow it fills my head with ideas-only I don't
know what they are!"
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