# Thread: Covariance matrices and better estimators

1. ## Covariance matrices and better estimators

Hello!
I have been looking at the following problem for a while now, and I can't seem to work my way through it.
It is about whether one estimator is better than another estimator. I think that rearranging the equation might be useful but I cant get to what I think is the end.
Thank you

2. ## Re: Covariance matrices and better estimators

Hey JuliaP.

Do you understand what makes a better estimator in terms of variance/covariance?

3. ## Re: Covariance matrices and better estimators

Originally Posted by JuliaP
Hello!
I have been looking at the following problem for a while now, and I can't seem to work my way through it.
It is about whether one estimator is better than another estimator. I think that rearranging the equation might be useful but I cant get to what I think is the end.
Thank you
the piece of info you need is that

$\lambda_{min} \|a\|^2 \leq a^T V a \leq \lambda_{max} \| a \|^2$

where $\lambda_{min}, ~\lambda_{max}$ are the smallest and largest eigenvalues of $V$ respectively

So basically the best estimator is the one whose covariance matrix has the smallest maximum eigenvalue.

4. ## Re: Covariance matrices and better estimators

Thanks so much for this:-)