Factorization theorem, Advanced Statistics

The theorem relating structure of the likelihood to the concept of the sufficient statistic. Officially the necessary and sufficient condition which a statistic S be sufficient for the parameter θ is that the likelihood, l(θ; y) can be expressed in the form given below;

2357_factorization theorem.png 

For instance, if Y1; Y2; ... ; Yn are the independent random variables from the Poisson distribution with the mean of μ, the likelihood is given by the following formula;

550_factorization theorem1.png 
which can be factorized into the following equation


1741_factorization theorem2.png

 

Posted Date: 7/27/2012 7:17:57 AM | Location : United States







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