# Expected value of the natural log of a ratio of variances [closed]

I am dealing with a one-way random effects model and am looking for the $E(\ln(\hat{\sigma}_\alpha^2/\hat{\sigma}^2))$ where $\hat{\sigma}_\alpha^2$ is the estimate of the between group variance and $\hat{\sigma}^2$ is the estimate of the error variance.

I am basically just interested in what a good estimate of the bias would be. I know from Jensen's inequality that it is negatively biased.

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I changed the tag to statistics, but I'm not sure if that's correct. – Zev Chonoles Jun 30 '11 at 17:19
I assume what you intended was the expected log ratio of the estimates of the variances? – cardinal Jun 30 '11 at 17:42
@cardinal: I see you are a high-rep user on stats.SE, so I will take your advice and migrate this question. – Zev Chonoles Jun 30 '11 at 17:48
@cardinal: yes, estimates of the variances – user5239 Jun 30 '11 at 18:02
@Kari Please, register your account on this site. You will then be able to link it to math.SE. – chl Jun 30 '11 at 19:55
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## closed as not a real question by whuber♦Aug 24 '11 at 14:08

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.