I thought it dealt with these ok—could you be more specific?
It’s linear because it’s an expectation. It is under-specified in that it needs us to assume or prove the marginal distributions for the Xi and I guess that’s problematic if an algorithm for doing that is a big part of what the authors are looking for. But if we do have marginal distributions for each Xi, then E(X2i),E(X′2i),E(X′2i|π′) are well-defined and ~E(∑ni=1X2i|π)=∑ni=1E(X′2i|π′).
How does your hereustic estimator deal with sums of squares? Is it linear?
I thought it dealt with these ok—could you be more specific?
It’s linear because it’s an expectation. It is under-specified in that it needs us to assume or prove the marginal distributions for the Xi and I guess that’s problematic if an algorithm for doing that is a big part of what the authors are looking for. But if we do have marginal distributions for each Xi, then E(X2i),E(X′2i),E(X′2i|π′) are well-defined and ~E(∑ni=1X2i|π)=∑ni=1E(X′2i|π′).