BTW --- and this is a diversion ---  This is nice mathematically
     (and used in other places, also in "base R" I think)
but in principle is a waste:  Computing a full
k x k matrix and then throwing away all but the length-k
diagonal ...
In the past I had contemplated but never RFC'ed or really
implemented a stderr() generic with default method

    stderr.default <- function(object) sqrt(diag(vcov(object)))

but allow non-default methods to be smarter and hence more efficient.

A fine idea for sure, but perhaps use a different name in order to avoid conflicts with:

> base::stderr
function ()
.Internal(stderr())
<bytecode: 0x32e1e98>
<environment: namespace:base>

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