As I show in the examples in DSLT1, having degenerate Fisher information (i.e. degenerate Hessian at zeroes) comes in two essential flavours: having rank-deficiency, and having vanishing second-derivative (i.e. K(w)=w4). Precisely, suppose d is the number of parameters, then you are in the regular case if K(w) can be expressed as a full-rank quadratic form near each singularity,
K(w)=d∑i=1w2i.
Anything less than this is a strictly singular case.
So if K(w)=w2, then w=0 is a singularity but not a strict singularity, do you agree? It still feels like somewhat bad terminology to me, but maybe it’s justified from the algebraic-geometry—perspective.
Thanks for the reply!
So if K(w)=w2, then w=0 is a singularity but not a strict singularity, do you agree? It still feels like somewhat bad terminology to me, but maybe it’s justified from the algebraic-geometry—perspective.