Precisely representing an irrational number in integer-base arithmetic is of course impossible. I do not ask that Stata be able to do this. Nor do I ask that Stata implement CAS, rather than floating point arithmetic, to solve such systems exactly. Nor do I ask that Stata violate IEEE 754-2008.
What I ask, basically, is that Stata flush denormal numbers to positive zero (FTZ) in this self-contained context (i.e. VCV matrices and intermediate matrices produced by Stata regression commands). This would not be implemented in floating-point arithmetic, but rather in a discrete procedure following these matrix operations. In other words, I am asking Stata to assume that any variance estimated in this way and with magnitude smaller than something like 1e-31 is in fact equal to zero. I think this assumption would virtually always be correct, and in a highly implausible situation where it is incorrect it will be only one of many such errors.
What I ask, basically, is that Stata flush denormal numbers to positive zero (FTZ) in this self-contained context (i.e. VCV matrices and intermediate matrices produced by Stata regression commands). This would not be implemented in floating-point arithmetic, but rather in a discrete procedure following these matrix operations. In other words, I am asking Stata to assume that any variance estimated in this way and with magnitude smaller than something like 1e-31 is in fact equal to zero. I think this assumption would virtually always be correct, and in a highly implausible situation where it is incorrect it will be only one of many such errors.
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