Notes

2025-1-5:

Note: theta hat has poor notation, because implicitly dependent on the sample.

suppose replace hat theta itself?
- replace with something that does not depend on the sample?
- what would it be?

- approximation that might work?
-- in SRS, is E[hat theta] = theta star?
-- if g is differentiable, g maybe approximated at g' at theta*?


even FI, usually want it to be bounded away from 0.
- otherwise, error explodes.
-- so, potentially we can put a condition on the g.
-- the choice of the g function has to be such that it can't be identifiability
---- identifiability issues.
---- if we do not lower bound the gs, then can be zero.
---- so, likely will make a lower bound of the g-expression. and then get the expression of the ESS.
------ then, see if LB goes to zero, if ESS goes to zero.
------ reverse Lipschitz condition?
^ check that this makes for some simple cases?? does it become nonsensical?
-------- logistic? get back to the problem


potentially can also just leave rho^2_{R, G} on its own as well!


making this equivalence more explicit soon.

to-do:
- think more about how to intuitively explain the scenarios, and WHY selecting abs(Y) should lead to dependencies between the d.d.c. and sample elasticity?