content_image/312114.jpg content_image/312111.jpg content_image/312112.jpg content_image/312113.jpg content_image/312115.jpg content_image/312110.jpg
Let H I U and H I V be the fixed marginal entropies of the partition I : 

<img src='content_image/312114.jpg'>

where C$_{x}$ ( I ) and C$_{y}$ ( I ) are the intervals induced by I in x and in y , respectively. Note that given I , the observed and expected margins of the partitions are fixed, and therefore 

<img src='content_image/312111.jpg'>

<img src='content_image/312112.jpg'>

<img src='content_image/312113.jpg'>

<img src='content_image/312115.jpg'>

The following simple derivation shows that the likelihood ratio score T I is a linear combination of ˆ H I $_{UV}$,H I U and H I $_{V}$: 

where the last equality follows from equations (B.2) and (B.4). 

<img src='content_image/312110.jpg'>

