# How to interpet this equation? [closed]

Can I get some help on interpreting this equation? Is it saying which ever section separated by the commma is bigger would be the answer? How do you intepret Sigma pi= 1? Thanks!

• Well one answer is $\Sigma_{i=1}^n p_i$ What does $U_i(\cdot,\cdot)$ refer to? If you reduce that ambiguity we may be able to help more. – Carl Apr 25 '20 at 4:37

$$U$$ is the score function. The solution to the sum of scores equal to 0 is a generalized estimating equation. $$p$$ is a set of possible probability weights.
You are trying to find the set of $$p$$ that maximizes their product, since $$n$$ is a constant and can be factored outside of the product. Without the constraint that $$\beta$$ is actually a solution to the GEE, we'd expect $$p=1/n$$ i.e. the unweighted GEE to be the solution. But if $$\beta$$ is set to something different, there may be a set of weights for which that is the solution.
$$R$$ is commonly referred to as a risk function, which is the expected loss. As an example, for quadratic loss, $$R$$ is the MSE of an estimator.
The supremum is maximizing the quantity $$\prod_{i=1}^n np_i$$ subject to all the constraints after the colon, and separated by commas. So, it's maximizing $$\prod_{i=1}^n np_i$$ subject to \begin{align*} \sum_{i=1}^np_iU_i(\beta,t)&=0,\;\text{and}\\ p_i&\ge 0\;\forall\,1\le i\le n,\;\text{and}\\ \sum_{i=1}^n p_i&=1. \end{align*} The last two conditions merely imply that the $$p_i$$ form a probability distribution.