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Thread: Covariance matrices and better estimators

  1. #1
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    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
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  2. #2
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    Re: Covariance matrices and better estimators

    Hey JuliaP.

    Do you understand what makes a better estimator in terms of variance/covariance?
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  3. #3
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    Re: Covariance matrices and better estimators

    Quote Originally Posted by JuliaP View Post
    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.
    Thanks from JuliaP
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    Re: Covariance matrices and better estimators

    Thanks so much for this:-)
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