# Maximum likelihood estimator variance

Hi,

I have an estimator:

p=1/nt * ∑Xi , and I need to find its variance, but I'm unsure of how to go about it.

Any pointers?

Thanks
Original post by econhelp525
Hi,

I have an estimator:

p=1/nt * ∑Xi , and I need to find its variance, but I'm unsure of how to go about it.

Any pointers?

Thanks

Is that the full question, are you told about the underlying distribution (normal/binomial/...)? But the starting point is the usual variance formula.
(edited 2 years ago)
Original post by econhelp525
Hi,

I have an estimator:

p=1/nt * ∑Xi , and I need to find its variance, but I'm unsure of how to go about it.

Any pointers?

Thanks

You need to calculate the negative reciprocal of the Fisher information. Have you done that?
Original post by mqb2766
Is that the full question, are you told about the underlying distribution (normal/binomial/...)? But the starting point is the usual variance formula.

It's usual, when talking about the variance of the MLE, to consider the asymptotic variance assuming the central limit theorem holds.
Original post by mqb2766
Is that the full question, are you told about the underlying distribution (normal/binomial/...)? But the starting point is the usual variance formula.

Yes, sorry, it follows a binomial distribution, where p is the estimate.

Original post by Gregorius
You need to calculate the negative reciprocal of the Fisher information. Have you done that?

That's the second part of the question, to use the Fisher Information.

Just to clarify, Var(X)=-1/I(θ), where I(θ)=-E{∂^2/∂θ^2} ?

The first part of the question we are told just to calculate the variance, and got: [p(1-p)]/t , but this doesn't look right, as when I searched up a solution, it's meant to be over n not t.