🚀 go-pugleaf

In article <1992Aug16.212245.27577@mailhost.ocs.mq.edu.au> wskelly@laurel.ocs.m
q.edu.au (William Skelly) writes:
[deletions]
>
>This and other posting indicate that there is a relationship between
>sample size and and estimated variance (of the population) which is
>positive and always an underestimate.  What is the limit, or point
>at which an increasing sample size no longer improve the estimate
>of populations variance?
                      ___  _         _
(1) the statistic T=  \   | X - Xbar  | 2                              __  2
                      /__ |_         _|         has expectation (n-1) O
       __ 2
where O    denotes the population variance  *for any value of n*. Therefore,
    T                                   __ 2
------------    is always unbiased for O     and    T
   n - 1                                         -------
                                                    n

                         __ 2
will always have bias - O             regardless of the value of n.
                      _____
                        n

Expectation is a linear operator. Note that the bias --> 0 as n gets large,
but T/n is biased for all finite n.

(2) The variance of the unbiased estimator T/(n-1) is O(1/n), so taking
a large sample will be beneficial in the sense of leading to an estimator
with smaller variance.

>Can this be tested by taking samples of sample (the later sample
>being elevated to the status of population)?

(3) I'm not clear what your mean here, this sounds something like
bootstrapping / jackknifing (well-known words for well-known techniques
which are not well-understood. . . )

Robert George
(speaking only for myself)