Thread: What is the sufficient statistic for bivariate normal?

1. What is the sufficient statistic for bivariate normal?

What is the sufficient statistic for bivariate normal if the covariance matrix is known.
Thanks!
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?

2. Re: What is the sufficient statistic for bivariate normal?

Originally Posted by hehe1223
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?

3. Re: What is the sufficient statistic for bivariate normal?

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

By factorization theorem.

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