[personal profile] barking_iguana
I have a class C of objects. I have a sample of objects of the class. And each object O has its own sample with a number of trials NO. NO has a range of 1 to several hundred.

Each object O has a parameter PO. What I want is the variance of PO in the class C.

The true values of PO are not known. But from each object's sample, I have XO, which is an estimate of PO. And I have VO, which is the variance of XO as an estimate of PO, given NO. (I don't know if XO is an unbiased estimator, but if need be, I can use a function f where f(XO) is very close to an unbiased estimator of f(PO).)



I think this is something I ought to know how to do. Or at least be able to find the answer via Google. But so far, no such luck. And it's not just curiosity this time, but a business need.

Note that I can't just take the variance of XO, because the limited sample size NO means that each XO contains variability both from the variance of PO (which is what I'm looking for) and from the variance of XO as an estimate. If I already knew the class variance of PO, I could use that to refine my estimate of PO for each object. But I'm trying to do more or less the reverse of that.
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