Re: Corollary: N-P Silliness in Estimation Theory (was: Re: Unusual formulae for confidence intervals)


David Jones wrote:
Reef Fish wrote:

But in a sense the MOST "peculiar" of all these concepts is the
N-P theorists' pre-occupation of the notion of an UNBIASED estimate.
E(statistic) = population parameter to be estimated.

Here, E ( SSE/(n-1)) = sigma^2, hence an unbiased estimate.

but the SQUARE ROOT of S^2 is a BAISED estimate of sigma
whether you use n, (n-1), or (n+1) as the denominator.


On the other hand, scaling by (n-1) is in line with the usual scaling
in regression by subtracting the number of degrees of freedom (total
number of regreesors including 1 for the intercept) used in the model
from the sample size.

But that's only the layman's heuristics without any understanding of
the THEORY of estimation behind all the estimators. In the regression
case, the estimators are all of the UNBIASED class (in variance), and
suffers the same silliness when used for confidence intervals using
the square root for standard error, it's NO LONGER unbiased!

-- Reef Fish Bob.


In this case the scaling at least means that,
for a given fixed sample, the estimate of the error variance remains
stable as the number of regressors increases, assuming that these have
no explanatory power.

David Jones

.

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