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    What is the sufficient statistic for bivariate normal?

    What is the sufficient statistic for bivariate normal if the covariance matrix is known.
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    I am puzzled about this. From the definition of sufficient statistics, it seems that 2 df chi-square statistic is the sufficient statistic. But since there are two means, the sufficient statistic should be 2 dimensional?
    Last edited by Dason; 04-10-2011 at 07:27 PM.

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    Re: What is the sufficient statistic for bivariate normal?

    Quote Originally Posted by hehe1223 View Post
    From the definition of sufficient statistics, it seems that 2 df chi-square statistic is the sufficient statistic.
    How exactly do you make that argument?

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    Re: What is the sufficient statistic for bivariate normal?

    Quote Originally Posted by Dason View Post
    How exactly do you make that argument?
    f(x|theta)=f(t|theta)*h(x)

    By factorization theorem.

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