You’ve left out the condition for the theorem to be true that the region with non-zero probabilitiy density can’t vary with the parameter.
That’s how, for example, the uniform distribution over (0,theta) can have a scalar sufficient statistic (the maximum data point) desipite it not being an exponential family model.
You’ve left out the condition for the theorem to be true that the region with non-zero probabilitiy density can’t vary with the parameter.
That’s how, for example, the uniform distribution over (0,theta) can have a scalar sufficient statistic (the maximum data point) desipite it not being an exponential family model.
Good catch, thanks.