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Eli Luong
science forum beginner
Joined: 24 Mar 2006
Posts: 18
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 Posted: Thu Jun 29, 2006 12:23 am Post subject:
point estimation of variance
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I was given two different equations to calculate the variance from a
sample. The equation is as follows:
(sum_of (Xi - x_bar)^2) / ( n -1 )
It's taking the sum of the square of the difference between each x_i
and the average value, then dividing by (n-1).
The mle, maximum likelihood estimation, was the same, but (n-1) was
substituted with an n.
I was wondering under what conditions would I use to determine which
one to use. The first is unbiased, and the second is not, but the
second is the mle, whereas the first is not.
Thanks,
- Eli |
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Herman Rubin
science forum Guru
Joined: 25 Mar 2005
Posts: 730
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| Posted: Thu Jun 29, 2006 7:30 pm Post subject:
Re: point estimation of variance
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In article <1151540625.550114.253590@75g2000cwc.googlegroups.com>,
Eli Luong <eliluong@gmail.com> wrote:
| Quote: | I was given two different equations to calculate the variance from a
sample. The equation is as follows:
(sum_of (Xi - x_bar)^2) / ( n -1 )
It's taking the sum of the square of the difference between each x_i
and the average value, then dividing by (n-1).
The mle, maximum likelihood estimation, was the same, but (n-1) was
substituted with an n.
I was wondering under what conditions would I use to determine which
one to use. The first is unbiased, and the second is not, but the
second is the mle, whereas the first is not.
|
It depends on the use. If one wants the best estimate
from the standpoint of mean squared error, divide by n+1.
The advantage of dividing by n-1 is that this can be used
for further purposes. A classic paper of Neyman and Scott
considers the case in which one has samples of size n_j
with means mu_j but a common variance v. The mle of v
is
\sum (sum_of (Xij - x_bar_j)^2) / \sum n_j
which is not a good estimator, but replacing n_j by n_j-1 is.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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