### Statistics Question

May. 17th, 2016 03:38 pm**barking_iguana**

I have a class

Each object

The true values of

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

*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*N*._{O}*N*has a range of 1 to several hundred._{O}Each object

*O*has a parameter*P*._{O}**What I want is the variance of***P*in the class_{O}*C*.The true values of

*P*are not known. But from each object's sample, I have_{O}*X*, which is an estimate of_{O}*P*. And I have_{O}*V*, which is the variance of_{O}*X*as an estimate of_{O}*P*, given_{O}*N*. (I don't know if_{O}*X*is an unbiased estimator, but if need be, I can use a function_{O}*f*where*f(X*is very close to an unbiased estimator of_{O})*f(P*.)_{O})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

*X*, because the limited sample size_{O}*N*means that each_{O}*X*contains variability both from the variance of_{O}*P*(which is what I'm looking for) and from the variance of_{O}*X*as an estimate. If I already knew the class variance of_{O}*P*, I could use that to refine my estimate of_{O}*P*for each object. But I'm trying to do more or less the reverse of that._{O}