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

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. 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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